SQL Reloaded: Data Management Views for the Synapse serverless SQL pool (& Microsoft Fabric Warehouse)

Unfortunately, the Dynamic Management Views (DMVs) for serverless SQL Server pools don't seem to be documented (or at least I haven't found them in the standard SQL Server documentation). I was thinking some weeks back how I could retrieve them easily as cursors aren't supported in serverless. In the end the old-fashioned loop got the job done (even if might not be the best way to do it):

 

-- retrieving the data management views in use with the number of records they held
DECLARE @view_name nvarchar(150)
DECLARE @sql nvarchar(250)
DECLARE @number_records bigint 
DECLARE @number_views int, @iterator int

DROP TABLE IF EXISTS dbo.#views;

CREATE TABLE dbo.#views (
  ranking int NOT NULL
, view_name nvarchar(150) NOT NULL
)

INSERT INTO #views
SELECT row_number() OVER(ORDER BY object_id) ranking
, concat(schema_name(schema_id),'.', name) view_name
FROM sys.all_views obj
WHERE obj.Type = 'V'
  AND obj.is_ms_shipped = 1
  --AND obj.name LIKE 'dm_exec_requests%'
ORDER BY view_name
SET @iterator = 1
SET @number_views = IsNull((SELECT count(*) FROM #views), 0)

WHILE (@iterator <= @number_views)
BEGIN 
    SET @view_name = (SELECT view_name FROM #views WHERE ranking = @iterator)
    SET @sql = CONCAT(N'SELECT @NumberRecords = count(*) FROM ', @view_name)

	BEGIN TRY
		--get the number of records
		EXEC sp_executesql @Query = @sql
		, @params = N'@NumberRecords bigint OUTPUT'
		, @NumberRecords = @number_records OUTPUT

		IF IsNull(@number_records, 0)> 0  
		BEGIN
		  SELECT @view_name, @number_records
		END 
	END TRY
	BEGIN CATCH  
	 -- no action needed in case of error
        END CATCH;

	SET @iterator = @iterator + 1
END

DROP TABLE IF EXISTS dbo.#views;

As can be seen the code above retrieves the system views and dumps them in a temporary table, then loops through each record and for each record retrieves the number of records available with the sp_executesql. The call to the stored procedure is included in a TRY/CATCH block to surpress the error messages, considering that many standard SQL Server DMVs are not supported. The error messages follow the same pattern: 

Msg 15871, Level 16, State 9, Line 187
DMV (Dynamic Management View) 'dm_resource_governor_resource_pool_volumes' is not supported. 

 On the instance I tested the code, from a total of 729 DMVs only 171 records were returned, though maybe there are some views not shown because the feature related to them was not yet configured:

 

View name	Description
INFORMATION_SCHEMA.COLUMNS	Returns one row for each column (*)
INFORMATION_SCHEMA.PARAMETERS	Returns one row for each parameter of a user-defined function or stored procedure (*)
INFORMATION_SCHEMA.ROUTINE_COLUMNS	Returns one row for each column returned by the table-valued functions (*)
INFORMATION_SCHEMA.ROUTINES	Returns one row for each stored procedure and function (*)
INFORMATION_SCHEMA.SCHEMATA	Returns one row for each schema in the current database
INFORMATION_SCHEMA.TABLES	Returns one row for each table or view in the current database (*)
INFORMATION_SCHEMA.VIEW_COLUMN_USAGE	Returns one row for each column in the current database that is used in a view definition
INFORMATION_SCHEMA.VIEW_TABLE_USAGE	Returns one row for each table in the current database that is used in a view
INFORMATION_SCHEMA.VIEWS	Returns one row for each view that can be accessed by the current user in the current database
sys.all_columns
sys.all_objects
sys.all_parameters
sys.all_sql_modules
sys.all_views
sys.allocation_units
sys.assemblies
sys.assembly_files
sys.assembly_types
sys.columns
sys.configurations
sys.credentials
sys.data_spaces
sys.database_automatic_tuning_options
sys.database_automatic_tuning_options_internal
sys.database_credentials
sys.database_files
sys.database_filestream_options
sys.database_mirroring
sys.database_mirroring_endpoints
sys.database_permissions
sys.database_principals
sys.database_query_store_internal_state
sys.database_query_store_options
sys.database_recovery_status
sys.database_resource_governor_workload_groups
sys.database_role_members
sys.database_scoped_configurations
sys.database_scoped_credentials
sys.databases
sys.dm_exec_connections
sys.dm_exec_query_stats
sys.dm_exec_requests	Returns information about each request that is executing in SQL Server.
sys.dm_exec_requests_history	Returns information about each request that executed in SQL Server; provided by Microsoft for troubleshooting.
sys.dm_exec_sessions
sys.dm_external_data_processed
sys.dm_os_host_info
sys.dm_request_phases	Returns information about each request phase performed in request's execution.
sys.dm_request_phases_exec_task_stats	Returns information about each task performed in request's execution.
sys.dm_request_phases_task_group_stats	Returns information aggregated at task group level about each task performed in request's execution.
sys.endpoints
sys.event_notification_event_types
sys.extended_properties
sys.external_data_sources
sys.external_file_formats
sys.external_language_files
sys.external_languages
sys.external_table_columns
sys.external_tables
sys.filegroups
sys.fulltext_document_types
sys.fulltext_languages
sys.fulltext_system_stopwords
sys.identity_columns
sys.index_columns
sys.indexes
sys.internal_tables
sys.key_encryptions
sys.linked_logins
sys.login_token
sys.master_files
sys.messages
sys.objects
sys.parameters
sys.partitions
sys.procedures
sys.query_store_databases_health
sys.query_store_global_health
sys.resource_governor_configuration
sys.resource_governor_external_resource_pools
sys.resource_governor_resource_pools
sys.resource_governor_workload_groups
sys.routes
sys.schemas
sys.securable_classes
sys.server_audit_specification_details
sys.server_audit_specifications
sys.server_audits
sys.server_event_session_actions
sys.server_event_session_events
sys.server_event_session_fields
sys.server_event_session_targets
sys.server_event_sessions
sys.server_memory_optimized_hybrid_buffer_pool_configuration
sys.server_permissions
sys.server_principals
sys.server_role_members
sys.servers
sys.service_contract_message_usages
sys.service_contract_usages
sys.service_contracts
sys.service_message_types
sys.service_queue_usages
sys.service_queues
sys.services
sys.spatial_reference_systems
sys.sql_dependencies
sys.sql_expression_dependencies
sys.sql_logins
sys.sql_modules
sys.stats
sys.stats_columns
sys.symmetric_keys
sys.sysaltfiles
sys.syscacheobjects
sys.syscharsets
sys.syscolumns
sys.syscomments
sys.sysconfigures
sys.syscurconfigs
sys.sysdatabases
sys.sysdepends
sys.sysfilegroups
sys.sysfiles
sys.sysindexes
sys.sysindexkeys
sys.syslanguages
sys.syslockinfo
sys.syslogins
sys.sysmembers
sys.sysmessages
sys.sysobjects
sys.sysoledbusers
sys.sysperfinfo
sys.syspermissions
sys.sysprocesses
sys.sysprotects
sys.sysservers
sys.system_columns
sys.system_components_surface_area_configuration
sys.system_internals_allocation_units
sys.system_internals_partition_columns
sys.system_internals_partitions
sys.system_objects
sys.system_parameters
sys.system_sql_modules
sys.system_views
sys.systypes
sys.sysusers
sys.tables
sys.tcp_endpoints
sys.time_zone_info
sys.trace_categories
sys.trace_columns
sys.trace_event_bindings
sys.trace_events
sys.trace_subclass_values
sys.trigger_event_types
sys.type_assembly_usages
sys.types
sys.user_token
sys.via_endpoints
sys.views
sys.xml_schema_attributes
sys.xml_schema_collections
sys.xml_schema_component_placements
sys.xml_schema_components
sys.xml_schema_facets
sys.xml_schema_model_groups
sys.xml_schema_namespaces
sys.xml_schema_types
sys.xml_schema_wildcards

Notes:
1) As can be seen, also the INFORMATION_SCHEMA views don't seem to be fully supprted.
2) "(*)" in description marks the views that can be accessed by the current user in the current database.

3) I removed the number of records as they are instance specific.
4) The code should work also on a dedicated SQL Server pool.
5) I hope to come back and showcase the usage of some of the most important views. 

6) The script can be used for the Microsoft Fabric Warehouse, however each record will be shown in a different panel! One can use an additional temporary table to save the results or extend the views table and update the table with the result, like in the following script:

-- retrieving the data management views in use with the number of records they held
DECLARE @view_name nvarchar(150)
DECLARE @sql nvarchar(250)
DECLARE @number_records bigint 
DECLARE @number_views int, @iterator int

DROP TABLE IF EXISTS dbo.#views;

CREATE TABLE dbo.#views (
  ranking int NOT NULL
, view_name nvarchar(150) NOT NULL
, record_count bigint NULL
)

INSERT INTO #views
SELECT row_number() OVER(ORDER BY object_id) ranking
, concat(schema_name(schema_id),'.', name) view_name
, NULL record_count
FROM sys.all_views obj
WHERE obj.Type = 'V'
  AND obj.is_ms_shipped = 1
  --AND obj.name LIKE 'dm_exec_requests%'
ORDER BY view_name

SET @iterator = 1
SET @number_views = IsNull((SELECT count(*) FROM #views), 0)

WHILE (@iterator <= @number_views)
BEGIN 
    SET @view_name = (SELECT view_name FROM #views WHERE ranking = @iterator)
    SET @sql = CONCAT(N'SELECT @NumberRecords = count(*) FROM ', @view_name)

	BEGIN TRY
		--get the number of records
		EXEC sp_executesql @Query = @sql
		, @params = N'@NumberRecords bigint OUTPUT'
		, @NumberRecords = @number_records OUTPUT

		IF IsNull(@number_records, 0)>= 0  
		BEGIN
		  UPDATE #views
                  SET record_count = @number_records
                  WHERE view_name = @view_name
		END 
	END TRY
	BEGIN CATCH  
	 -- no action needed in case of error
    END CATCH;

	SET @iterator = @iterator + 1
END

SELECT *
FROM dbo.#views;

DROP TABLE IF EXISTS dbo.#views;

Happy coding!

Systems Engineering: Self-Organization (Just the Quotes)

"Clearly, if the state of the system is coupled to parameters of an environment and the state of the environment is made to modify parameters of the system, a learning process will occur. Such an arrangement will be called a Finite Learning Machine, since it has a definite capacity. It is, of course, an active learning mechanism which trades with its surroundings. Indeed it is the limit case of a self-organizing system which will appear in the network if the currency supply is generalized." (Gordon Pask, "The Natural History of Networks", 1960)

"It is inherent in the logical character of the abstract self-organizing system that all available methods of organization are used, and that it cannot be realized in a single reference frame. Thus, any of the tricks which the physical model can perform, such as learning and remembering, may be performed by one or all of a variety of mechanisms, chemical or electrical or mechanical." (Gordon Pask, "The Natural History of Networks", 1960)

"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […]  'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"In self-organizing systems, on the other hand, ‘control’ of the organization is typically distributed over the whole of the system. All parts contribute evenly to the resulting arrangement." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium.” (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

“To adapt to a changing environment, the system needs a variety of stable states that is large enough to react to all perturbations but not so large as to make its evolution uncontrollably chaotic. The most adequate states are selected according to their fitness, either directly by the environment, or by subsystems that have adapted to the environment at an earlier stage. Formally, the basic mechanism underlying self-organization is the (often noise-driven) variation which explores different regions in the system’s state space until it enters an attractor. This precludes further variation outside the attractor, and thus restricts the freedom of the system’s components to behave independently. This is equivalent to the increase of coherence, or decrease of statistical entropy, that defines self-organization." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"[The] system may evolve through a whole succession of transitions leading to a hierarchy of more and more complex and organized states. Such transitions can arise in nonlinear systems that are maintained far from equilibrium: that is, beyond a certain critical threshold the steady-state regime become unstable and the system evolves into a new configuration." (Ilya Prigogine, Gregoire Micolis & Agnes Babloyantz, "Thermodynamics of Evolution", Physics Today 25 (11), 1972)

"There is nothing supernatural about the process of self-organization to states of higher entropy; it is a general property of systems, regardless of their materials and origin. It does not violate the Second Law of thermodynamics since the decrease in entropy within an open system is always offset by the increase of entropy in its surroundings." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Every system of whatever size must maintain its own structure and must deal with a dynamic environment, i.e., the system must strike a proper balance between stability and change. The cybernetic mechanisms for stability (i.e., homeostasis, negative feedback, autopoiesis, equifinality) and change (i.e., positive feedback, algedonodes, self-organization) are found in all viable systems." (Barry Clemson, "Cybernetics: A New Management Tool", 1984)

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

"Complex adaptive systems have the property that if you run them - by just letting the mathematical variable of 'time' go forward - they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously. [...] A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life. (J Doyne Farmer, "The Third Culture: Beyond the Scientific Revolution", 1995)

"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems. […] Self-organization provides a paradigm for behavior and cognition, as well as the structure and function of the nervous system. In contrast to a computer, which requires particular programs to produce particular results, the tendency for self-organization is intrinsic to natural systems under certain conditions." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)

"[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations." (Fritjof  Capra, "The web of life: a new scientific understanding of living  systems", 1996)

"Emergent self-organization in multi-agent systems appears to contradict the second law of thermodynamics. This paradox has been explained in terms of a coupling between the macro level that hosts self-organization (and an apparent reduction in entropy), and the micro level (where random processes greatly increase entropy). Metaphorically, the micro level serves as an entropy 'sink', permitting overall system entropy to increase while sequestering this increase from the interactions where self-organization is desired." (H Van Dyke Parunak & Sven Brueckner, "Entropy and Self-Organization in Multi-Agent Systems", Proceedings of the International Conference on Autonomous Agents, 2001)

"In principle, a self-organising system cannot be constructed, since its organisation and behaviour cannot be prescribed and created by an external source. It emerges autonomously in certain conditions (which cannot be prescribed either). The task of the researcher is to investigate in what kind of systems and under what kind of conditions self-organisation emerges." (Rein Vihalemm, "Chemistry as an Interesting Subject for the Philosophy of Science", 2001)

"Self-organization [is] the appearance of structure or pattern without an external agent imposing it." (Francis Heylighen, "The science of Self-organization and Adaptivity", 2001)

"Through self-organization, the behavior of the group emerges from the collective interactions of all the individuals. In fact, a major recurring theme in swarm intelligence (and of complexity science in general) is that even if individuals follow simple rules, the resulting group behavior can be surprisingly complex - and remarkably effective. And, to a large extent, flexibility and robustness result from self-organization." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"[…] swarm intelligence is becoming a valuable tool for optimizing the operations of various businesses. Whether similar gains will be made in helping companies better organize themselves and develop more effective strategies remains to be seen. At the very least, though, the field provides a fresh new framework for solving such problems, and it questions the wisdom of certain assumptions regarding the need for employee supervision through command-and-control management. In the future, some companies could build their entire businesses from the ground up using the principles of swarm intelligence, integrating the approach throughout their operations, organization, and strategy. The result: the ultimate self-organizing enterprise that could adapt quickly - and instinctively - to fast-changing markets." (Eric Bonabeau & Christopher Meyer, "Swarm Intelligence: A Whole New Way to Think About Business", Harvard Business Review, 2001)

"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"This spontaneous emergence of order at critical points of instability is one of the most important concepts of the new understanding of life. It is technically known as self-organization and is often referred to simply as ‘emergence’. It has been recognized as the dynamic origin of development, learning and evolution. In other words, creativity-the generation of new forms-is a key property of all living systems. And since emergence is an integral part of the dynamics of open systems, we reach the important conclusion that open systems develop and evolve. Life constantly reaches out into novelty." (Fritjof  Capra, "The Hidden Connections", 2002)

"A self-organizing system not only regulates or adapts its behavior, it creates its own organization. In that respect it differs fundamentally from our present systems, which are created by their designer. We define organization as structure with function. Structure means that the components of a system are arranged in a particular order. It requires both connections, that integrate the parts into a whole, and separations that differentiate subsystems, so as to avoid interference. Function means that this structure fulfils a purpose." (Francis Heylighen & Carlos Gershenson, "The Meaning of Self-organization in Computing", IEEE Intelligent Systems, 2003)

"The basic concept of complexity theory is that systems show patterns of organization without organizer (autonomous or self-organization). Simple local interactions of many mutually interacting parts can lead to emergence of complex global structures. […] Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or 'punctuations' of all sizes. In the critical state, events which would otherwise be uncoupled became correlated." (Jochen Fromm, "The Emergence of Complexity", 2004)

"A system described as self-organizing is one in which elements interact in order to achieve dynamically a global function or behavior." (Carlos Gershenson, "A general methodology for designing self-organizing systems", 2006)

"Like resilience, self-organizazion is often sacrificed for purposes of short-term productivity and stability." (Donella H Meadows, “Thinking in Systems: A Primer”, 2008)

"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"In engineering, a self-organizing system would be one in which elements are designed to dynamically and autonomously solve a problem or perform a function at the system level. In other words, the engineer will not build a system to perform a function explicitly, but elements will be engineered in such a way that their behaviour and interactions will lead to the system function. Thus, the elements need to divide, but also to integrate, the problem." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"Nature is capable of building complex structures by processes of self-organization; simplicity begets complexity." (Victor J Stenger, God: "The Failed Hypothesis", 2010)

"Cybernetics studies the concepts of control and communication in living organisms, machines and organizations including self-organization. It focuses on how a (digital, mechanical or biological) system processes information, responds to it and changes or being changed for better functioning (including control and communication)." (Dmitry A Novikov, "Cybernetics 2.0", 2016)

More quotes on "Self-Organization" at the-web-of-knowledge.blogspot.com.

Systems Engineering: Feedback (Just the Quotes)

"Feedback is a method of controlling a system by reinserting into it the results of its past performance. If these results are merely used as numerical data for the criticism of the system and its regulation, we have the simple feedback of the control engineers. If, however, the information which proceeds backward from the performance is able to change the general method and pattern of performance, we have a process which may be called learning." (Norbert Wiener, 1954)

"[...] the concept of 'feedback', so simple and natural in certain elementary cases, becomes artificial and of little use when the interconnexions between the parts become more complex. When there are only two parts joined so that each affects the other, the properties of the feedback give important and useful information about the properties of the whole. But when the parts rise to even as few as four, if every one affects the other three, then twenty circuits can be traced through them; and knowing the properties of all the twenty circuits does not give complete information about the system. Such complex systems cannot be treated as an interlaced set of more or less independent feedback circuits, but only as a whole. For understanding the general principles of dynamic systems, therefore, the concept of feedback is inadequate in itself. What is important is that complex systems, richly cross-connected internally, have complex behaviours, and that these behaviours can be goal-seeking in complex patterns." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Traditional organizational theories have tended to view the human organization as a closed system. This tendency has led to a disregard of differing organizational environments and the nature of organizational dependency on environment. It has led also to an over-concentration on principles of internal organizational functioning, with consequent failure to develop and understand the processes of feedback which are essential to survival." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by non‐linear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive‐feedback loops describing growth processes as well as negative, goal‐seeking loops." (Jay W Forrester, "Urban Dynamics", 1969)

"To model the dynamic behavior of a system, four hierarchies of structure should be recognized: closed boundary around the system; feedback loops as the basic structural elements within the boundary; level variables representing accumulations within the feedback loops; rate variables representing activity within the feedback loops." (Jay W Forrester, "Urban Dynamics", 1969)

"Effect spreads its 'tentacles' not only forwards (as a new cause giving rise to a new effect) but also backwards, to the cause which gave rise to it, thus modifying, exhausting or intensifying its force. This interaction of cause and effect is known as the principle of feedback. It operates everywhere, particularly in all self-organising systems where perception, storing, processing and use of information take place, as for example, in the organism, in a cybernetic device, and in society. The stability, control and progress of a system are inconceivable without feedback." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Ultimately, uncontrolled escalation destroys a system. However, change in the direction of learning, adaptation, and evolution arises from the control of control, rather than unchecked change per se. In general, for the survival and co-evolution of any ecology of systems, feedback processes must be embodied by a recursive hierarchy of control circuits." (Bradford P Keeney, "Aesthetics of Change", 1983)

"Every system of whatever size must maintain its own structure and must deal with a dynamic environment, i.e., the system must strike a proper balance between stability and change. The cybernetic mechanisms for stability (i.e., homeostasis, negative feedback, autopoiesis, equifinality) and change (i.e., positive feedback, algedonodes, self-organization) are found in all viable systems." (Barry Clemson, "Cybernetics: A New Management Tool", 1984) 

"The term closed loop-learning process refers to the idea that one learns by determining what s desired and comparing what is actually taking place as measured at the process and feedback for comparison. The difference between what is desired and what is taking place provides an error indication which is used to develop a signal to the process being controlled." (Harold Chestnut, 1984) 

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the ‘best’ one."  (W Brian Arthur, "Returns and Path Dependence in the Economy", 1994)

“[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations.” (Fritjof  Capra, “The web of life: a new scientific understanding of living  systems”, 1996)

"Something of the previous state, however, survives every change. This is called in the language of cybernetics (which took it form the language of machines) feedback, the advantages of learning from experience and of having developed reflexes." (Guy Davenport, "The Geography of the Imagination: Forty Essays", 1997)

"Cybernetics is the science of effective organization, of control and communication in animals and machines. It is the art of steersmanship, of regulation and stability. The concern here is with function, not construction, in providing regular and reproducible behaviour in the presence of disturbances. Here the emphasis is on families of solutions, ways of arranging matters that can apply to all forms of systems, whatever the material or design employed. [...] This science concerns the effects of inputs on outputs, but in the sense that the output state is desired to be constant or predictable – we wish the system to maintain an equilibrium state. It is applicable mostly to complex systems and to coupled systems, and uses the concepts of feedback and transformations (mappings from input to output) to effect the desired invariance or stability in the result." (Chris Lucas, "Cybernetics and Stochastic Systems", 1999)

"All dynamics arise from the interaction of just two types of feedback loops, positive (or self-reinforcing) and negative (or self-correcting) loops. Positive loops tend to reinforce or amplify whatever is happening in the system […] Negative loops counteract and oppose change." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Much of the art of system dynamics modeling is discovering and representing the feedback processes, which, along with stock and flow structures, time delays, and nonlinearities, determine the dynamics of a system. […] the most complex behaviors usually arise from the interactions (feedbacks) among the components of the system, not from the complexity of the components themselves." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

“The phenomenon of emergence takes place at critical points of instability that arise from fluctuations in the environment, amplified by feedback loops." (Fritjof Capra, "The Hidden Connections: A Science for Sustainable Living", 2002)

"Thus, nonlinearity can be understood as the effect of a causal loop, where effects or outputs are fed back into the causes or inputs of the process. Complex systems are characterized by networks of such causal loops. In a complex, the interdependencies are such that a component A will affect a component B, but B will in general also affect A, directly or indirectly.  A single feedback loop can be positive or negative. A positive feedback will amplify any variation in A, making it grow exponentially. The result is that the tiniest, microscopic difference between initial states can grow into macroscopically observable distinctions." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"The work around the complex systems map supported a concentration on causal mechanisms. This enabled poor system responses to be diagnosed as the unanticipated effects of previous policies as well as identification of the drivers of the sector. Understanding the feedback mechanisms in play then allowed experimentation with possible future policies and the creation of a coherent and mutually supporting package of recommendations for change."  (David C Lane et al, "Blending systems thinking approaches for organisational analysis: reviewing child protection", 2015)

More quotes on "Feedback" at the-web-of-knowledge.blogspot.com.

Systems Engineering: Networks (Just the Quotes)

"Any pattern of activity in a network, regarded as consistent by some observer, is a system." (Gordon Pask, "The Natural History of Networks", 1960)

"I am using the term 'network' in a general sense, to imply any set of interconnected and measurably active physical entities. Naturally occurring networks, of interest because they have a, self-organizing character, are, for example, a marsh, a colony of microorganisms, a research team, and a man." (Gordon Pask, "The Natural History of Networks", 1960)

"A NETWORK is a collection of connected lines, each of which indicates the movement of some quantity between two locations. Generally, entrance to a network is via a source (the starting point) and exit from a network is via a sink (the finishing point); the lines which form the network are called links (or arcs), and the points at which two or more links meet are called nodes." (Cecil W Lowe, "Critical Path Analysis by Bar Chart", 1966)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 1979)

"When loops are present, the network is no longer singly connected and local propagation schemes will invariably run into trouble. [...] If we ignore the existence of loops and permit the nodes to continue communicating with each other as if the network were singly connected, messages may circulate indefinitely around the loops and process may not converges to a stable equilibrium. […] Such oscillations do not normally occur in probabilistic networks […] which tend to bring all messages to some stable equilibrium as time goes on. However, this asymptotic equilibrium is not coherent, in the sense that it does not represent the posterior probabilities of all nodes of the network." (Judea Pearl, "Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference", 1988)

"What is a system? A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment." (William E Deming, "The New Economics for Industry, Government, Education”, 1993)

"Mathematics says the sum value of a network increases as the square of the number of members. In other words, as the number of nodes in a network increases arithmetically, the value of the network increases exponentially. Adding a few more members can dramatically increase the value of the network." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"The basic principle of an autocatalytic network is that even though nothing can make itself, everything in the pot has at least one reaction that makes it, involving only other things in the pot. It's a symbiotic system in which everything cooperates to make the metabolism work - the whole is greater than the sum of the parts." (J Doyne Farmer, "The Second Law of Organization" [in The Third Culture: Beyond the Scientific Revolution], 1995)

"The only organization capable of unprejudiced growth, or unguided learning, is a network. All other topologies limit what can happen." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"The multiplier effect is a major feature of networks and flows. It arises regardless of the particular nature of the resource, be it goods, money, or messages." (John H Holland, "Hidden Order - How Adaptation Builds Complexity", 1995)

"The more complex the network is, the more complex its pattern of interconnections, the more resilient it will be." (Fritjof Capra, "The Web of Life: A New Scientific Understanding of Living Systems", 1996)

"The notion of system we are interested in may be described generally as a complex of elements or components directly or indirectly related in a network of interrelationships of various kinds, such that it constitutes a dynamic whole with emergent properties." (Walter F. Buckley, "Society: A Complex Adaptive System - Essays in Social Theory", 1998)

"Remember a networked learning machine’s most basic rule: strengthen the connections to those who succeed, weaken them to those who fail." (Howard Bloom, "Global Brain: The Evolution of Mass Mind from the Big Bang to the 21st Century", 2000)

"[…] most earlier attempts to construct a theory of complexity have overlooked the deep link between it and networks. In most systems, complexity starts where networks turn nontrivial." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"One of the key insights of the systems approach has been the realization that the network is a pattern that is common to all life. Wherever we see life, we see networks." (Fritjof Capra, "The Hidden Connections: A Science for Sustainable Living", 2002)

"The networked world continuously refines, reinvents, and reinterprets knowledge, often in an autonomic manner." (Donald M Morris et al, "A revolution in knowledge sharing", 2003)

"Hierarchy adapts knowledge to the organization; a network adapts the organization to the knowledge." (George Siemens, "Knowing Knowledge", 2006)

"Nodes and connectors comprise the structure of a network. In contrast, an ecology is a living organism. It influences the formation of the network itself." (George Siemens, "Knowing Knowledge", 2006)

"If a network is solely composed of neighborhood connections, information must traverse a large number of connections to get from place to place. In a small-world network, however, information can be transmitted between any two nodes using, typically, only a small number of connections. In fact, just a small percentage of random, long-distance connections is required to induce such connectivity. This type of network behavior allows the generation of 'six degrees of separation' type results, whereby any agent can connect to any other agent in the system via a path consisting of only a few intermediate nodes." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"Networks may also be important in terms of view. Many models assume that agents are bunched together on the head of a pin, whereas the reality is that most agents exist within a topology of connections to other agents, and such connections may have an important influence on behavior. […] Models that ignore networks, that is, that assume all activity takes place on the head of a pin, can easily suppress some of the most interesting aspects of the world around us. In a pinhead world, there is no segregation, and majority rule leads to complete conformity - outcomes that, while easy to derive, are of little use." (John H Miller & Scott E Page, "Complex Adaptive Systems", 2007)

"We are beginning to see the entire universe as a holographically interlinked network of energy and information, organically whole and self-referential at all scales of its existence. We, and all things in the universe, are non-locally connected with each other and with all other things in ways that are unfettered by the hitherto known limitations of space and time." (Ervin László, "Cosmos: A Co-creator's Guide to the Whole-World", 2010)

"The people we get along with, trust, feel simpatico with, are the strongest links in our networks." (Daniel Goleman, "Working With Emotional Intelligence", 2011) 

"Cybernetics is the study of systems which can be mapped using loops (or more complicated looping structures) in the network defining the flow of information. Systems of automatic control will of necessity use at least one loop of information flow providing feedback." (Alan Scrivener, "A Curriculum for Cybernetics and Systems Theory", 2012)

"If we create networks with the sole intention of getting something, we won't succeed. We can't pursue the benefits of networks; the benefits ensue from investments in meaningful activities and relationships." (Adam Grant, "Give and Take: A Revolutionary Approach to Success", 2013) 

"Information is recorded in vast interconnecting networks. Each idea or image has hundreds, perhaps thousands, of associations and is connected to numerous other points in the mental network." (Peter Russell, "The Brain Book: Know Your Own Mind and How to Use it", 2013) 

"All living systems are networks of smaller components, and the web of life as a whole is a multilayered structure of living systems nesting within other living systems - networks within networks." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

"Although cascading failures may appear random and unpredictable, they follow reproducible laws that can be quantified and even predicted using the tools of network science. First, to avoid damaging cascades, we must understand the structure of the network on which the cascade propagates. Second, we must be able to model the dynamical processes taking place on these networks, like the flow of electricity. Finally, we need to uncover how the interplay between the network structure and dynamics affects the robustness of the whole system." (Albert-László Barabási, "Network Science", 2016)

"The exploding interest in network science during the first decade of the 21st century is rooted in the discovery that despite the obvious diversity of complex systems, the structure and the evolution of the networks behind each system is driven by a common set of fundamental laws and principles. Therefore, notwithstanding the amazing differences in form, size, nature, age, and scope of real networks, most networks are driven by common organizing principles. Once we disregard the nature of the components and the precise nature of the interactions between them, the obtained networks are more similar than different from each other." (Albert-László Barabási, "Network Science", 2016)

More quotes on "Networks" at the-web-of-knowledge.blogspot.com.

Systems Engineering: Feedback Loop (Definition)

"A feedback loop is a closed path of causal relations among variables. Feedback loops usually represent the process of monitoring the state of the system, the effects of decisions in the system state, and future decisions." (Luis F Luna-Reyes, "System Dynamics to Understand Public Information Technology", 2008)

"A circular chain of interactions, such that each element in the loop influences its own future level of activation. Feedback loops are also known as circuits." (Elizabeth Santiago-Cortés, "Discrete Networks as a Suitable Approach for the Analysis of Genetic Regulation", 2009)

"A feedback loop is a cycle in a directed graph whose edges can represent either positive or negative inputs." (Maria C A Leite & Yunjiao Wang, "Multistability, oscillations and bifurcations in feedback loops", Mathematical Biosciences and Engineering Vol 7 (1), 2010)

"A linked system of statements in a map in which the arrows show a path of links that feed back to the starting point. A feedback loop exists when the statements around the loop are all variables - that is, they can vary over time, typically increasing or decreasing, or getting better or worse. Feedback loops can be stable or generative (vicious or virtuous)." (Fran Ackermann et al, "Visual Strategy: Strategy Mapping for Public and Nonprofit Organizations", 2014)

[control *:] "A conceptual construct of control theory in which a comparison between a goal state and the measured current state drives a decision-making process for an action to bring the system closer to the goal state. The feedback loop increases the effectiveness of the defensive actions." (O Sami Saydjari, "Engineering Trustworthy Systems: Get Cybersecurity Design Right the First Time", 2018)

"A feedback loop is a sequence of variables and causal links that creates a closed ring of causal influences." (David N Ford, "A system dynamics glossary", System Dynamics Review Vol. 35 (4), 2019)

[balancing *:] "a feedback loop in which the resultant effect of the causal links over time limits or constrains the movement of variables. Balancing loops seek equilibrium, trying to bring stocks to a desired state and keep them there. Also called a negative, compensating, goal-seeking or controlling feedback loop." (David N Ford, "A system dynamics glossary", System Dynamics Review Vol. 35 (4), 2019)

[reinforcing *:] "a feedback loop in which the sum effect of the causal links tends to strengthen (reinforce) the movement of variable values in a given direction due to positive feedback." (David N Ford, "A system dynamics glossary", System Dynamics Review Vol. 35 (4), 2019)

"Is a closed chain pattern of cause and effect reaction connections from a stock, activated by decisions, rules, physical laws, or actions." (Tatiana C Valencia & Stephanie J Valencia, "Cultivating Flow and Happiness in Children", 2020)

"Feedback loop is defined as a system used to control the level of a variable in which there is an identifiable receptor (sensor), control center (integrator or comparator), effectors, and methods of communication." (Lumen Learning, Anatomy and Physiology I [course])

Graphical Representation: Causal Loop Diagrams (Definition)

"One of the tools of systems thinking. Causal loop diagrams capture how variables in a system are interrelated. A CLD takes the form of a closed loop that depicts cause-and-effect linkages." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Casual Loops", 1997)

"A CLD is a graphic model of some of the key system variables connected by arrows that denote the causal influences among the variables. Each arrowhead is identified as either positive (+) or negative (-) to indicate how the dependent variable changes when the independent variable changes." (Daniel D Burke, System Dynamics-based Computer Simulations and Evaluation, 2006)

"A CLD is diagrammatic tool used to describe the causal relationship between key quantities and to identify feedback mechanisms." (Dina Neiger & Leonid Churilov, "Integration of Diagrammatic Business Modeling Tools", 2008)

"A network of actuators connected together is called a causal loop diagram. A causal loop diagram shows how potential business actions lead to complex dynamic effects." (David M Bridgeland & Ron Zahavi, "Business Modeling: A Practical Guide to Realizing Business Value", 2009)

"A tool that captures the causal interrelationships amongst a set of variables. CLDs reveal systemic patterns underlying complex relationships and highlight hidden causes and unintended consequences." (Kambiz E Maani, "Systems Thinking and the Internet from Independence to Interdependence", 2009)

"Causal loop diagramming is a form of cause-and-effect modeling. The diagrams represent systems and their behaviors as a collection of nodes and links. Nodes represent the things in a system, and links illustrate interactions and influences." (Olivia Parr Rudd, "Business Intelligence Success Factors: Tools for Aligning Your Business in the Global Economy", 2009)

"Causal loop diagrams (CLDs) are a kind of systems thinking tool. These diagrams consist of arrows connecting variables (things that change over time) in a way that shows how one variable affects another." (Raed M Al-Qirem & Saad G Yaseen, "Modelling a Small Firm in Jordan Using System Dynamics", 2010)

"A visual representation of a system's feedback loops, where positive loops cycle clockwise, and negative loops cycle counter-clockwise." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"In systems thinking terms, causal loop diagrams are simplified ways to describe essential elements and relationships in a system. These diagrams include curved causal-link arrows (depicting influence from cause to effect) and the polarity of that linkage. An 's' indicates that cause and effect move in the same direction and an  'o' shows that they move in opposite directions (e.g., when cause increases, effect decreases below what it would have been). Causal-link arrows combine into balancing (B) and reinforcing (R) feedback loops. Significant lags between an action and the effects of that action appear as 'delay' on the causal-link arrows." (Karen L Higgins, "Economic Growth and Sustainability: Systems Thinking for a Complex World", 2015)

"A causal loop diagram (CLD) is a causal diagram that aids in visualizing how a number of variables in a system are interrelated and drive cause-and-effect processes. The diagram consists of a set of nodes and edges. Nodes represent the variables, and edges are the links that represent a connection or a relation between the two variables." (Andreas F Vermeulen, "Practical Data Science: A Guide to Building the Technology Stack for Turning Data Lakes into Business Assets", 2018)

"Methodology to build conceptual or simulation models depicting the causal structure of a complex system." (Francesca Costanza & Pietro Fontana, "Distributing Mutual Advantages in Italian Cooperatives: An Analysis of Patronage Refunds", 2019)

"In system dynamics modelling, they are closed causal chains involving relevant variables, whose interactions are responsible for the patterns of behavior taking place within a certain system." (Francesca Costanza, "Managing Patients' Organizations to Improve Healthcare: Emerging Research and Opportunities", 2020)

SQL Reloaded: Pulling the Strings of SQL Server IX (Special Characters)

    Under special characters denomination are categorized typically the characters that don’t belong to the alphabet of a given language, typically English (a-z, A-Z), or the numeric digits (0-9). Characters like umlauts (e.g. ä, ë, ö, ü, ÿ), accents (e.g. é, í, ó, ú) and other type of characters used in specific languages like German, French, Turkish, Hungarian, Romanian, Dutch or Swedish, together with punctuation signs or graphical characters are falling under the designation of special characters. It’s true that SQL Server, like many other databases, supports Unicode, a standard designed to encode such characters, though not all database designs are taking Unicodes into account. Preponderantly the old database and other software solutions use the non-unicode string data types (char, varchar, text) fact that makes the special characters to be displayed inadequately, sometimes undecipherable. In order to avoid this behavior could be decided to port the data types to unicode or use only the standard characters of English language, both solutions with their positive and negative aspects. In such cases, especially during migration project or ETL tasks, eventually as part of a Data Quality initiative, it’s preferred to identify and replace the special characters in a manual, automatic or semi-automatic fashion. In addition, there are also cases in which, from various reasons, some attributes are not allowed or should not include special characters, and also this aspect could be included in a Data Quality initiative.

    During assessment of Data Quality, in an organized or less organized manner, a first step resides in understanding the quality of the data. In the current case this resumes primarily in identifying how many records contain special characters, how could be the data cleaned, and the “cost” for this activity. Actually, before going this far, must be defined the character sets included in special characters, the definition could vary from case to case. For example in some cases could be considered also the space or the important punctuation signs as valid characters, while in others they may not be allowed. There could be identified thus multiple scenarios, though I found out that the range of characters a-z, A-Z, 0-9 and the space are considered as valid character in most of the cases. For this purpose could be built a simple function that iterates through all the characters of a string and identifies if there is any character not belonging to the before mentioned range of valid characters. In order to address this, a few years back I built a function similar with the below one:

-- checks if a string has special characters 
CREATE FUNCTION dbo.HasSpecialCharacters( 
@string nvarchar(1000)) 
RETURNS int 
AS  
    BEGIN 
         DECLARE @retval int 
         DECLARE @index int 
         DECLARE @char nchar(1)  

         SET @retval = 0 
         SET @index = 1  

         WHILE (@index <= IsNull(len(@string), 0) AND @retval=0) 
        BEGIN  
           SET @char = Substring(@string, @index, @index+1) 
           IF NOT (ASCII(@char) BETWEEN 48 AND 57 -- numeric value 
             OR ASCII(@char) BETWEEN 65 AND 90 -- capital letters 
            OR ASCII(@char) BETWEEN 97 AND 122 -- small letters 
            OR ASCII(@char) = 32) --space 
           BEGIN 
                SET @retval = @index 
           END 
           ELSE 
               SET @index = @index + 1  
     END  

    RETURN (@retval) 
END 

    Function’s logic is based on the observation that the ASCII of numeric values could be found in the integer interval between 48 and 57, the capital letters between 65 and 90, while the small letters between 97 and 122. By adding the ASCII for space and eventually several other characters, the check on whether an character is valid resuming thus to only 4 constraints. Here’s the function at work:  

-- testing HasSpecialCharacters function 
SELECT dbo.HasSpecialCharacters('kj324h5kjkj3245k2j3hkj342jj4') Example1 
, dbo.HasSpecialCharacters('Qualität') Example2 
, dbo.HasSpecialCharacters('Änderung') Example3 
, dbo.HasSpecialCharacters('') Example4 
, dbo.HasSpecialCharacters(NULL) Example5 
, dbo.HasSpecialCharacters('Ä') Example6 
, dbo.HasSpecialCharacters('ä') Example7 
, dbo.HasSpecialCharacters('a') Example8 

 


    As can be seen, the function returns the position where a special character is found, fact that enables users to identify the character that causes the problem. A similar function could be built also in order to count the number of special characters found in a string, the change residing in performing a counter rather then returning the position at the first occurrence of a special character.

    The function might not be perfect though it solves the problem. There are also other alternatives, for example of storing the special characters in a table and performing a simple join against the target table. Another solution could be based on the use RegEx functionality, either by using OLE automation or directly CLR functionality. There could be done variations on the above solution too by limiting to check on whether the characters of a string are falling in the range projected by the ASCII function. That’s what the following function does:  

-- checks if a string has special characters falling in an interval  
CREATE FUNCTION dbo.HasCharNotInASCIIRange( 
@string nvarchar(1000) 
, @start int 
, @end int) 
RETURNS int 
AS  
BEGIN      
    DECLARE @retval int 
    DECLARE @index int 
    DECLARE @char nchar(1) 

 
    SET @retval = 0 
    SET @index = 1 

    WHILE (@index <= IsNull(len(@string), 0) AND @retval=0) 
    BEGIN  
         SET @char = Substring(@string, @index, @index+1) 
         IF NOT (ASCII(@char) BETWEEN @start AND @end)  
        BEGIN 
              SET @retval = @index 
        END 
        ELSE 
             SET @index = @index + 1  
     END 
     RETURN (@retval) 
END 

         With this function are necessary 4 calls in order to identify if a string contains special characters, though we loose the flexibility of identifying the first character that is invalid. We could still identify the first occurrence by taking the minimum value returned by the 4 calls, however, unlike Oracle (see Least function), SQL Server doesn’t have such a function, so we’ll have eventually to built it. Anyway, here’s the above function at work:  

-- testing HasCharNotInASCIIRange function 
SELECT dbo.HasCharNotInASCIIRange('k12345', 48, 57) Example1 
, dbo.HasCharNotInASCIIRange('12k345', 48, 57) Example2 
, dbo.HasCharNotInASCIIRange('12345', 48, 57) Example3 
, dbo.HasCharNotInASCIIRange(' 12345', 48, 57) Example4 
, dbo.HasCharNotInASCIIRange('12345 ', 48, 57) Example5 
, dbo.HasCharNotInASCIIRange('', 48, 57) Example6 
, dbo.HasCharNotInASCIIRange(NULL, 48, 57) Example7 
, dbo.HasCharNotInASCIIRange('', 48, 57) Example8 
, dbo.HasCharNotInASCIIRange('a', 48, 57) Example9 
, dbo.HasCharNotInASCIIRange('Ä', 48, 57) Example10 
, dbo.HasCharNotInASCIIRange('ä', 32, 32) Example11