Joseph Sgro
Encyclopedia
Joseph A. Sgro is a mathematician
, neurologist
and a technologist/entrepreneur in the field of frame grabber
s, high speed smart camera
s, vision processors, and related computer vision
and machine vision
technologies.
Sgro began his career as an academic researcher in advanced mathematics and logic. He received an AB in Mathematics in 1970 from UCLA
followed by an MA in mathematics in 1973 and a PhD in mathematics in 1975 from the University of Wisconsin, where he studied logic model theory under H. Jerome Keisler
.
After serving as an instructor and post doctoral fellow at Yale
and also holding a membership at the Institute for Advanced Studies at Princeton University
, Sgro returned to school to study neurology, and received his M.D. in 1980 from the Leonard M. Miller School of Medicine
at the University of Miami
, followed by an internship and a residency in neurology.
As an outgrowth of his work in neurophysiology, while still working as a post-doctoral fellow and an assistant professor of neurology, Sgro founded Alacron, Inc. in 1985 to manufacture frame grabbers and related technologies to commercialize the technology built to support his academic research. Extending his work in machine vision technology, in 2002, Sgro founded FastVision, a maker of smart camera
s.
has completeness
, which had previously been widely believed but was not definitely established.
Sgro’s proof drew attention throughout mathematical world, and, in 1974, a year before finishing his PhD, he was awarded a three year appointment as a Josiah Willard Gibbs Instructor in Mathematics at Yale University and received an NSF research grant to continue his work in topological model theory. Wisconsin allowed him to accept this honor while remotely completing his thesis and dissertation at Wisconsin, which he did in 1975. His conclusions regarding the topological model theory formed the basis of his PhD thesis and dissertation. Published in in 1977, Sgro’s thesis “Completeness Theorems for Topological Models” also included additional theories by Sgro that were published in 1976 in the Israel Journal of Mathematics
. His work also resulted in an invitation to speak at the Logica Colloquim ’77 European Meeting of the Association for Symbolic Logic
. This event was held in Wrocław, Poland
, which was then still part of the Eastern Bloc
, making Sgro among the first mathematicians from the West to speak at an event “behind the Iron Curtain.” Sgro also spent 1977-1978 at the Institute for Advanced Study
at Princeton University
.
Key research includes:
, the branch of neurology
and physiology
that examines the functioning of the peripheral nervous system and cortical processing of sensory information. Neurophysiological research typically uses imaging tools for visualizing chemical activity in nerve pathways, and today also involves fMRI
and other technologies to visualize brain activity. After receiving his M.D. degree from Miami in 1980, Sgro completed his internship at the University of North Carolina
in 1981 and his residency in neurology at Columbia-Presbyterian Medical Center in 1984.
After serving as a post-doctoral fellow in neurophysiology (1983-1985), as an Associate in Neurology (1985-1986) and then as an Assistant Professor of Neurology (1986-1987) at The College of Physicians and Surgeons
at Columbia University
in New York City
, Sgro relocated to Richmond, Virginia
. There he served first as an Associate Professor of Neurology and as the Head of Neurophysiology (1987-1991) and finally, as Chief of the Division of Clinical Neurophysiology (1991-1994) at the Virginia Commonwealth University Medical Center
.
While working as a neurology researcher, Sgro focused increasingly on the use of machine vision technologies (especially frame grabbers) during surgery, to acquire graphical imagery measuring the operation of neurological function in various states of consciousness.
During his post-doctoral fellowship at Columbia-Presbyterian Medical Center, Sgro achieved recognition in the medical community for his research and findings on the theory of evoked potentials, with a particular focus on somatosensory evoked potentials
(SSEPs). He proved that SSEPs were “state dependent,” varying depending on whether the patient was awake or asleep (anesthetized). Following these findings, Sgro developed a more effective way to utilize the theory of evoked potentials by inventing technology and techniques to analyze ultra fast, pseudo-random evoked potentials. This work produced a more effective identification and treatment of sub-clinical diseases (diseases that otherwise went undetected and/or untreated until they become severe enough to qualify as clinical).
Achieving more effective detection and treatment of sub-clinical diseases involved increasingly intensive intra-operative patient monitoring. This research and the resulting findings stimulated Sgro’s interest in machine vision, specifically the use of frame grabbers to monitor neurological impulses during complex surgery.
To commercialize hardware developed initially for evoked potentials research, in 1985, Sgro co-founded Alacron, Inc. to do basic research and to build commercial medical imaging products such as frame grabbers. He was also appointed as an adjunct associate professor of Neurology at Columbia-Presbyterian Medical Center in 1994.
Sgro's research work resulted in the following publications and grants:
. Sgro and the Alacron engineering team focused on the development and production of frame grabber
s and high speed image processing computational subsystems. The product family currently includes frame grabbers, software, data recording devices and supporting peripherals. Despite initial focus on neurophysiology research and medical imaging, Alacron saw uses for its products expand outside the field of medicine into other applications, such as manufacturing, military, and other industries that use robotics extensively. Alacron is one of the two largest frame grabber manufacturers in the Automated Imaging Association
's annual market data report.
Examples of broader machine vision uses of frame grabbers originally developed for use in medical imaging include AS&E
, which incorporated Alacron technology in backscatter X-ray
equipment used for border security, and as image capture used for Voyage Data Recorder
s, the maritime equivalent of aviation “black box
es.”
In addition to the commercial product lines offered by Alacron, Sgro continued to perform basic research in integrating frame grabber technology with specialized systems for various disciplines. The company received SBIR
grants where Sgro acted as principal investigators, including:
Academic presentations of Alacron’s technology and research include:
s, cameras with high-speed scalable integrated processing capabilities built into the same package housing the optoelectronics. Like most smart camera vendors, FastVision’s suite includes integrated FPGA processing and memory subsystems to enable in-camera image processing. When integrated with a high powered frame grabber or vision processor board (or a host subsystem), the resulting system capabilities can be expanded beyond simple image compression. The smart camera subsystem can be integrated with disk or non-volatile semiconductor storage inside or outside the camera to hold sustained real-time data acquisition, a valuable aid to system effectiveness when network connectivity is overloaded or is unavailable.
Applications for smart cameras range from security and surveillance, to robotics in medicine and manufacturing, to military applications such as bots, drones and intelligent weaponry, to satellites and inner and outer space exploration.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, neurologist
Neurologist
A neurologist is a physician who specializes in neurology, and is trained to investigate, or diagnose and treat neurological disorders.Neurology is the medical specialty related to the human nervous system. The nervous system encompasses the brain, spinal cord, and peripheral nerves. A specialist...
and a technologist/entrepreneur in the field of frame grabber
Frame grabber
A frame grabber is an electronic device that captures individual, digital still frames from an analog video signal or a digital video stream. It is usually employed as a component of a computer vision system, in which video frames are captured in digital form and then displayed, stored or...
s, high speed smart camera
Smart camera
Although there are many definitions of smart cameras offered by the media, camera manufacturers and developers, still no binding definition exists. In a field where terms are often defined by their predominant usage, most material in this article is based on the term's most predominant usage...
s, vision processors, and related computer vision
Computer vision
Computer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...
and machine vision
Machine vision
Machine vision is the process of applying a range of technologies and methods to provide imaging-based automatic inspection, process control and robot guidance in industrial applications. While the scope of MV is broad and a comprehensive definition is difficult to distil, a "generally accepted...
technologies.
Sgro began his career as an academic researcher in advanced mathematics and logic. He received an AB in Mathematics in 1970 from UCLA
University of California, Los Angeles
The University of California, Los Angeles is a public research university located in the Westwood neighborhood of Los Angeles, California, USA. It was founded in 1919 as the "Southern Branch" of the University of California and is the second oldest of the ten campuses...
followed by an MA in mathematics in 1973 and a PhD in mathematics in 1975 from the University of Wisconsin, where he studied logic model theory under H. Jerome Keisler
Howard Jerome Keisler
H. Jerome Keisler is an American mathematician, currently professor emeritus at University of Wisconsin–Madison. His research has included model theory and non-standard analysis.His Ph.D...
.
After serving as an instructor and post doctoral fellow at Yale
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
and also holding a membership at the Institute for Advanced Studies at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, Sgro returned to school to study neurology, and received his M.D. in 1980 from the Leonard M. Miller School of Medicine
Leonard M. Miller School of Medicine
The University of Miami Leonard M. Miller School of Medicine is the school of medical education of the University of Miami. The main medical campus is located in the Civic Center, Miami, Florida within the UM/Jackson Memorial Medical Center complex...
at the University of Miami
University of Miami
The University of Miami is a private, non-sectarian university founded in 1925 with its main campus in Coral Gables, Florida, a medical campus in Miami city proper at Civic Center, and an oceanographic research facility on Virginia Key., the university currently enrolls 15,629 students in 12...
, followed by an internship and a residency in neurology.
As an outgrowth of his work in neurophysiology, while still working as a post-doctoral fellow and an assistant professor of neurology, Sgro founded Alacron, Inc. in 1985 to manufacture frame grabbers and related technologies to commercialize the technology built to support his academic research. Extending his work in machine vision technology, in 2002, Sgro founded FastVision, a maker of smart camera
Smart camera
Although there are many definitions of smart cameras offered by the media, camera manufacturers and developers, still no binding definition exists. In a field where terms are often defined by their predominant usage, most material in this article is based on the term's most predominant usage...
s.
Mathematical Research
During his first year as a PhD candidate at the University of Wisconsin, Sgro proved that the topological branch of model theoryModel theory
In mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
has completeness
Completeness
In general, an object is complete if nothing needs to be added to it. This notion is made more specific in various fields.-Logical completeness:In logic, semantic completeness is the converse of soundness for formal systems...
, which had previously been widely believed but was not definitely established.
Sgro’s proof drew attention throughout mathematical world, and, in 1974, a year before finishing his PhD, he was awarded a three year appointment as a Josiah Willard Gibbs Instructor in Mathematics at Yale University and received an NSF research grant to continue his work in topological model theory. Wisconsin allowed him to accept this honor while remotely completing his thesis and dissertation at Wisconsin, which he did in 1975. His conclusions regarding the topological model theory formed the basis of his PhD thesis and dissertation. Published in in 1977, Sgro’s thesis “Completeness Theorems for Topological Models” also included additional theories by Sgro that were published in 1976 in the Israel Journal of Mathematics
Israel Journal of Mathematics
Israel Journal of Mathematics is a peer-reviewed mathematics journal published by the Hebrew University of Jerusalem .Founded in 1963, as a continuation of the Bulletin of the Research Council of Israel , the journal publishes articles on all areas of mathematics.The journal is indexed by...
. His work also resulted in an invitation to speak at the Logica Colloquim ’77 European Meeting of the Association for Symbolic Logic
Association for Symbolic Logic
The Association for Symbolic Logic is an international organization of specialists in mathematical logic and philosophical logic—the largest such organization in the world. The ASL was founded in 1936, a crucial year in the development of modern logic, and its first president was Alonzo Church...
. This event was held in Wrocław, Poland
Poland
Poland , officially the Republic of Poland , is a country in Central Europe bordered by Germany to the west; the Czech Republic and Slovakia to the south; Ukraine, Belarus and Lithuania to the east; and the Baltic Sea and Kaliningrad Oblast, a Russian exclave, to the north...
, which was then still part of the Eastern Bloc
Eastern bloc
The term Eastern Bloc or Communist Bloc refers to the former communist states of Eastern and Central Europe, generally the Soviet Union and the countries of the Warsaw Pact...
, making Sgro among the first mathematicians from the West to speak at an event “behind the Iron Curtain.” Sgro also spent 1977-1978 at the Institute for Advanced Study
Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...
at Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
.
Key research includes:
- Completeness theorems for topological models, Annals of Mathematical Logic, Volume 11, Issue 2, August 1977, Pages 173-193, ISSN 0003-4843, 10.1016/0003-4843(77)90016-X.
Neurological Research
While researching mathematical logic, Sgro became interested in investigating the logic systems that the brain uses to process sensory information, and returned to school, intending to study neurophysiologyNeurophysiology
Neurophysiology is a part of physiology. Neurophysiology is the study of nervous system function...
, the branch of neurology
Neurology
Neurology is a medical specialty dealing with disorders of the nervous system. Specifically, it deals with the diagnosis and treatment of all categories of disease involving the central, peripheral, and autonomic nervous systems, including their coverings, blood vessels, and all effector tissue,...
and physiology
Physiology
Physiology is the science of the function of living systems. This includes how organisms, organ systems, organs, cells, and bio-molecules carry out the chemical or physical functions that exist in a living system. The highest honor awarded in physiology is the Nobel Prize in Physiology or...
that examines the functioning of the peripheral nervous system and cortical processing of sensory information. Neurophysiological research typically uses imaging tools for visualizing chemical activity in nerve pathways, and today also involves fMRI
Functional magnetic resonance imaging
Functional magnetic resonance imaging or functional MRI is a type of specialized MRI scan used to measure the hemodynamic response related to neural activity in the brain or spinal cord of humans or other animals. It is one of the most recently developed forms of neuroimaging...
and other technologies to visualize brain activity. After receiving his M.D. degree from Miami in 1980, Sgro completed his internship at the University of North Carolina
University of North Carolina
Chartered in 1789, the University of North Carolina was one of the first public universities in the United States and the only one to graduate students in the eighteenth century...
in 1981 and his residency in neurology at Columbia-Presbyterian Medical Center in 1984.
After serving as a post-doctoral fellow in neurophysiology (1983-1985), as an Associate in Neurology (1985-1986) and then as an Assistant Professor of Neurology (1986-1987) at The College of Physicians and Surgeons
Columbia University College of Physicians and Surgeons
Columbia University College of Physicians and Surgeons, often known as P&S, is a graduate school of Columbia University that is located on the health sciences campus in the Washington Heights neighborhood of Manhattan...
at Columbia University
Columbia University
Columbia University in the City of New York is a private, Ivy League university in Manhattan, New York City. Columbia is the oldest institution of higher learning in the state of New York, the fifth oldest in the United States, and one of the country's nine Colonial Colleges founded before the...
in New York City
New York City
New York is the most populous city in the United States and the center of the New York Metropolitan Area, one of the most populous metropolitan areas in the world. New York exerts a significant impact upon global commerce, finance, media, art, fashion, research, technology, education, and...
, Sgro relocated to Richmond, Virginia
Richmond, Virginia
Richmond is the capital of the Commonwealth of Virginia, in the United States. It is an independent city and not part of any county. Richmond is the center of the Richmond Metropolitan Statistical Area and the Greater Richmond area...
. There he served first as an Associate Professor of Neurology and as the Head of Neurophysiology (1987-1991) and finally, as Chief of the Division of Clinical Neurophysiology (1991-1994) at the Virginia Commonwealth University Medical Center
VCU Medical Center
VCU Medical Center, is Virginia Commonwealth University's medical campus located in downtown Richmond, Virginia in the Court End neighborhood. The VCU Medical Center used to be known as the Medical College of Virginia until it merged with the Richmond Professional Institute in 1968 to create...
.
While working as a neurology researcher, Sgro focused increasingly on the use of machine vision technologies (especially frame grabbers) during surgery, to acquire graphical imagery measuring the operation of neurological function in various states of consciousness.
During his post-doctoral fellowship at Columbia-Presbyterian Medical Center, Sgro achieved recognition in the medical community for his research and findings on the theory of evoked potentials, with a particular focus on somatosensory evoked potentials
Somatosensory Evoked Potential
Somatosensory Evoked Potentials are a useful, noninvasive means of assessing somatosensory system functioning. By combining SEP recordings at different levels of the somatosensory pathways, it is possible to assess the transmission of the afferent volley from the periphery up to the cortex...
(SSEPs). He proved that SSEPs were “state dependent,” varying depending on whether the patient was awake or asleep (anesthetized). Following these findings, Sgro developed a more effective way to utilize the theory of evoked potentials by inventing technology and techniques to analyze ultra fast, pseudo-random evoked potentials. This work produced a more effective identification and treatment of sub-clinical diseases (diseases that otherwise went undetected and/or untreated until they become severe enough to qualify as clinical).
Achieving more effective detection and treatment of sub-clinical diseases involved increasingly intensive intra-operative patient monitoring. This research and the resulting findings stimulated Sgro’s interest in machine vision, specifically the use of frame grabbers to monitor neurological impulses during complex surgery.
To commercialize hardware developed initially for evoked potentials research, in 1985, Sgro co-founded Alacron, Inc. to do basic research and to build commercial medical imaging products such as frame grabbers. He was also appointed as an adjunct associate professor of Neurology at Columbia-Presbyterian Medical Center in 1994.
Sgro's research work resulted in the following publications and grants:
- The Development of Methods for the Analysis of Non-Time-Stable Brain Responses. Whitaker FoundationWhitaker FoundationThe Whitaker Foundation was based in Arlington, Virginia and was an organization that primarily supported biomedical engineering education and research, but also supported other forms of medical research. It was founded and funded by U. A. Whitaker in 1975 upon his death with additional support...
grant, 1985-1989. - Phase synchronized triggering: A method for coherent noise elimination in evoked potential recording, Electroencephalography and Clinical Neurophysiology, Volume 60, Issue 5, May 1985, Pages 464-468, ISSN 0013-4694, 10.1016/0013-4694(85)91021-1.
- Real-time reconstruction of evoked potentials using a new two-dimensional filter method, Electroencephalography and Clinical Neurophysiology (Evoked Potentials Section), Volume 62, Issue 5, September 1985, Pages 372-380, ISSN 0168-5597, 10.1016/0168-5597(85)90046-2.
- Assessment of Afferent and Efferent Neuropathways in Severe Head Injury. NIH Program Project Grant #2P01NS012587, 1989-1992.
- Pathophysiology and Mortality of Status Epilepticus in Central Nervous System. NIH Program Grant #1P01NS025630-01A1, 1989-1998.
- Conventional and rapid stimulation evoked potential changes in patients with status epilepticus, Epilepsy Research, Volume 15, Issue 2, June 1993, Pages 149-156, ISSN 0920-1211, 10.1016/0920-1211(93)90095-O.
Alacron, Inc.
In 1985, Sgro co-founded Alacron, Inc. in Nashua, New HampshireNashua, New Hampshire
-Climate:-Demographics:As of the census of 2010, there were 86,494 people, 35,044 households, and 21,876 families residing in the city. The population density was 2,719.9 people per square mile . There were 37,168 housing units at an average density of 1,202.8 per square mile...
. Sgro and the Alacron engineering team focused on the development and production of frame grabber
Frame grabber
A frame grabber is an electronic device that captures individual, digital still frames from an analog video signal or a digital video stream. It is usually employed as a component of a computer vision system, in which video frames are captured in digital form and then displayed, stored or...
s and high speed image processing computational subsystems. The product family currently includes frame grabbers, software, data recording devices and supporting peripherals. Despite initial focus on neurophysiology research and medical imaging, Alacron saw uses for its products expand outside the field of medicine into other applications, such as manufacturing, military, and other industries that use robotics extensively. Alacron is one of the two largest frame grabber manufacturers in the Automated Imaging Association
Automated Imaging Association
Automated Imaging Association is the world's largest machine vision trade group. AIA has more than 300 members from 30 countries, including system integrators, camera, lighting and other vision components manufacturers, vision software providers, OEMs and distributors...
's annual market data report.
Examples of broader machine vision uses of frame grabbers originally developed for use in medical imaging include AS&E
American Science and Engineering
American Science and Engineering Inc, is a US manufacturer of X-ray equipment and related technologies, originating in 1958 as a developer for NASA, with an early focus on X-ray astronomy led by Riccardo Giacconi...
, which incorporated Alacron technology in backscatter X-ray
Backscatter X-ray
Backscatter X-ray is an advanced X-ray imaging technology. Traditional X-ray machines detect hard and soft materials by the variation in transmission through the target. In contrast, backscatter X-ray detects the radiation that reflects from the target...
equipment used for border security, and as image capture used for Voyage Data Recorder
Voyage Data Recorder
thumb|A fixed Data Capsule of VDR mounted on a [[container ship]].Voyage Data Recorder, or VDR, is a data recording system designed for all vessels required to comply with the IMO's International Convention SOLAS Requirements in order to collect data from various sensors on board the vessel...
s, the maritime equivalent of aviation “black box
Black Box (transportation)
The term black box is a placeholder name used casually to refer to a collection of several different recording devices used in transportation: the flight recorders in aircraft, the event recorder in railway locomotives, the event data recorder in automobiles, message case in ships, and other...
es.”
In addition to the commercial product lines offered by Alacron, Sgro continued to perform basic research in integrating frame grabber technology with specialized systems for various disciplines. The company received SBIR
Small Business Innovation Research
The Small Business Innovation Research program is a United States Government program, coordinated by the Small Business Administration, in which 2.5% of the total extramural research budgets of all federal agencies with extramural research budgets in excess of $100 million are reserved for...
grants where Sgro acted as principal investigators, including:
- "A Digital Signal Processing Evoked Potential Machine” NIHNational Institutes of HealthThe National Institutes of Health are an agency of the United States Department of Health and Human Services and are the primary agency of the United States government responsible for biomedical and health-related research. Its science and engineering counterpart is the National Science Foundation...
SBIR #1R44NS024494. 1986 (Phase 1), 1988-1990 (Phase 2). - "A Self Optimizing Evoked Potential Amplifier,” NIH SBIR #1R43NS24490. 1986-1987 (Phase 1), 1989-1991 (Phase 2).
- "A Magnetic Stimulator for Neurophysiology," NIH SBIR #1R43NS24924, 1986-1987 (Phase 1); 1989-1991 (Phase 2).
- "An Event Detecting Video/EEG Monitoring System,” NlH SBIR #1R43NS26204 , 1988-1989.
- "A Magnetic Neural Stimulator for Neurophysiology," NIH SBIR II #2R44NS24924, 1989-1991.
- ”An Efficient Lossless EEG Compression Engine,” NIH SBIR #1R43NS34211. 1995-1997 (phase 1); 1999-2003 (phase 2).
- "Scalable Programmable Accelerator for Affordable High Performance Computing,” DARPA Contract #N66001-96-C-8611, 1997-2001.
Academic presentations of Alacron’s technology and research include:
- "Vision Solutions for Life Sciences Applications" at Pittcon, 2006.
FastVision, LLC
In 2002, Sgro launched FastVision, LLC. FastVision builds high-speed megapixel-plus digital cameras, based on CMOS imagers. The company's goal is to produce smart cameraSmart camera
Although there are many definitions of smart cameras offered by the media, camera manufacturers and developers, still no binding definition exists. In a field where terms are often defined by their predominant usage, most material in this article is based on the term's most predominant usage...
s, cameras with high-speed scalable integrated processing capabilities built into the same package housing the optoelectronics. Like most smart camera vendors, FastVision’s suite includes integrated FPGA processing and memory subsystems to enable in-camera image processing. When integrated with a high powered frame grabber or vision processor board (or a host subsystem), the resulting system capabilities can be expanded beyond simple image compression. The smart camera subsystem can be integrated with disk or non-volatile semiconductor storage inside or outside the camera to hold sustained real-time data acquisition, a valuable aid to system effectiveness when network connectivity is overloaded or is unavailable.
Applications for smart cameras range from security and surveillance, to robotics in medicine and manufacturing, to military applications such as bots, drones and intelligent weaponry, to satellites and inner and outer space exploration.
Related Topics
- Evoked potentialEvoked potentialAn evoked potential is an electrical potential recorded from the nervous system of a human or other animal following presentation of a stimulus, as distinct from spontaneous potentials as detected by electroencephalography or electromyography .Evoked potential amplitudes tend to be low, ranging...
- Frame grabberFrame grabberA frame grabber is an electronic device that captures individual, digital still frames from an analog video signal or a digital video stream. It is usually employed as a component of a computer vision system, in which video frames are captured in digital form and then displayed, stored or...
s - Journal of Symbolic LogicJournal of Symbolic LogicThe Journal of Symbolic Logic is a peer-reviewed mathematics journal published quarterly by Association for Symbolic Logic.Founded in 1936, the journal publishes articles on mathematical logic....
- Lindström%27s theorem
- Löwenheim–Skolem theoremLöwenheim–Skolem theoremIn mathematical logic, the Löwenheim–Skolem theorem, named for Leopold Löwenheim and Thoralf Skolem, states that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ...
- Machine visionMachine visionMachine vision is the process of applying a range of technologies and methods to provide imaging-based automatic inspection, process control and robot guidance in industrial applications. While the scope of MV is broad and a comprehensive definition is difficult to distil, a "generally accepted...
- Model theoryModel theoryIn mathematics, model theory is the study of mathematical structures using tools from mathematical logic....
- NeurophysiologyNeurophysiologyNeurophysiology is a part of physiology. Neurophysiology is the study of nervous system function...