Professor Uziel Sandler | Lev Academic Center (original) (raw)

Papers by Professor Uziel Sandler

h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of... more h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of the system and the dynamics laws. • Evolution of these systems is equivalent to Generalized Lagrangian Mechanics. • Approach does not depend on specific properties of the system and may be equally applied to non-physical systems. • Principal of least action is a consequence of the causality principle and the local topology of the state space.

h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of... more h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of the system and the dynamics laws. • Evolution of these systems is equivalent to Generalized Lagrangian Mechanics. • Approach does not depend on specific properties of the system and may be equally applied to non-physical systems. • Principal of least action is a consequence of the causality principle and the local topology of the state space.

Journal of Clinical Oncology, Jun 1, 2023

A new approach to description of the global behavior of a fizzy system with information on short ... more A new approach to description of the global behavior of a fizzy system with information on short term evolution is proposed and investigated. The approach is based on the fuzzy master equation. For continuous evolution the digerential equations describing the flows of the fizzy state w obtained. Two cases of Kweak and strong fizziness" are considered.

Physica D: Nonlinear Phenomena, Jul 1, 2019

In this study, we extended our previous Lagrangian Fuzzy dynamics (S-Lagrangian dynamics) to the ... more In this study, we extended our previous Lagrangian Fuzzy dynamics (S-Lagrangian dynamics) to the systems of fields. Unlike common Lagrangian dynamics, additional "ghost"-fields, which have dual roles, appear in S-Lagrangian dynamics equations. These fields design hierarchical structures of a system and generate "ghost"-forces. In addition, the dynamics of these fields could lead to time irreversibility of the dynamics equations. Because the inference of S-Lagrangian equations is based only the causality principle, the common local topology of a system's state space, and assumptions that infinite velocities are impossible and that the system's state can be described by a compact fuzzy set, S-Lagrangian dynamics can be applied to physical and nonphysical systems as well. We applied S-Lagrangian dynamics to describe the behavior of populations of living species in the environment, assuming that the system's Lagrangian is defined by the dependence of velocity of changing of the population's stress on population densities, food supply, and environmental damage. The results show that even the first approximation of the Lagrangian allows the description of almost all types of species co-evolution: competition, coexistence, prey-predator dynamics, and ecological catastrophes.

Physica D: Nonlinear Phenomena, Nov 1, 2017

 Many-body system with S-dependent Lagrangian inevitably develops a hierarchical structure.  La... more  Many-body system with S-dependent Lagrangian inevitably develops a hierarchical structure.  Lagrangian and energy of these systems are vector functions, while conjugated momenta are second-order tensors.  Dominance hierarchies are determined by differences between individuals in coping with stress.

Social Science Research Network, 2022

Physical Review Letters, Apr 10, 1995

We have developed a theory of a phase transition under pressure in materials made from fibers. Us... more We have developed a theory of a phase transition under pressure in materials made from fibers. Using the path integral technique the free energy of the system is calculated. It is shown that a first order phase transition takes place and that the behavior of the thermodynamic parameters in the ordered phase are in accordance with scaling laws. Experimental data for leather agree qualitatively with the theory.

Physics Letters, Oct 1, 1988

ABSTRACT There exists a large population whose speech is considerably impaired and effectively un... more ABSTRACT There exists a large population whose speech is considerably impaired and effectively unintelligible. This group includes children as well as adults. The lack of successful human communication which they experience is a severe limitation and can even adversely affect their cognitive and social development. The goal of this work is to create a compact and stand alone system for online audio-translation of discrete impaired speech. Such a handy voice-input voice-output communication aid (VIVOCA) does not presently exist on the market. To this end, an appropriate method was developed for handicapped speech recognition. The system consists of two units: one module for recording and preprocessing the handicapped person's speech, based on a PC computer; and a stand alone, portable device for on-line recognition and translation based on a modified neural network. The procedure of translation takes about 0.5 sec., and the testing gives about 90% accuracy

Fuzzy Sets and Systems, Aug 1, 1999

We propose a description of continuous evolution of systems with uncertainty based on min or prod... more We propose a description of continuous evolution of systems with uncertainty based on min or product t-norms of fuzzy logic. We show that the dynamics has a Hamiltonian form in the extended state space composed from "physical" and "information" components if the min t-norm is used. This description is useful when available information on a system behavior is mainly ordinal and not numerical. If the product t-norm is used, the dynamics on a continuous universe is similar to the dynamics of stochastic processes , but the probability distribution is replaced by a possibility density. We show, that such replacement leads to an essential extension of the stochastic process theory. The differential equation of evolution of the possibility density cover most basic dynamics equations in physics.

arXiv (Cornell University), Mar 7, 2022

In this paper we consider generalization of classical/quantum mechanics that directly follows fro... more In this paper we consider generalization of classical/quantum mechanics that directly follows from the causality principle and topology of a system's state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the same, but the Hamiltonian may depend on the action and its canonically conjugated variables as additional dynamical variables. This extension of quantum mechanics indicates that the quantization of matter could be an evolutionary process, and in the distant future, even massive bodies may become entirely quantum objects without welldefined trajectories and shapes. In the classical limit, the first approximation of the Hamiltonian with respect to the action explains the accelerated expansion of the Universe, Hubble's law, formation of spiral galaxies with a non-Kepler curve of rotation velocity, and asymmetry between distributions of matter and antimatter. This theory predicts that our open universe could have extended prehistory and be preceded by a long set of closed precursor universes.

International Journal of Biological Macromolecules, Nov 1, 2010

In this paper we propose a theory, which considers the behavior of a circular macromolecule neari... more In this paper we propose a theory, which considers the behavior of a circular macromolecule nearing its transition phase to a condensed state. In particular, the explicit dependence of the phase transition characteristics on the macromolecule's topology is discussed. An important example of a circular macromolecule is bacterial DNA, and although the crystalline state appears incompatible with life, simple organisms use crystallization of DNA for protection against varied environmental assaults. It is shown that the cellular conditions that determine super-helical properties regulate the packaging of DNA as well and, therefore, regulate bacterial endurance and virulence.

Neurocomputing, 1997

... a) Initial state of network is far enough from correlated embedded patterns, (b) initial stat... more ... a) Initial state of network is far enough from correlated embedded patterns, (b) initial state ofnetwork is near ... The dj = a(.(ckj o) y) are linear net gains, 6 = 0((ckj (o) y; (c uo) y) are ... Then for ck, WQ K we can omit the indexes in the linear net gain and saturation coefficients in (8.1). ...

Physica D: Nonlinear Phenomena, Dec 1, 2014

In this paper, we show how to study the evolution of a complex system, given imprecise knowledge ... more In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1n+1n+1-dimensional space, where nnn is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics.

We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to \emph{non-physical} systems. An example of such an application is presented as well.

Fuzzy Sets and Systems, Nov 1, 1996

The global behavior of a system with information on fuzzy-described short-term evolution laws is ... more The global behavior of a system with information on fuzzy-described short-term evolution laws is proposed and investigated in the paper. For deterministic or stochastic models such problems are solved by use of differential equations describing the short-term laws. But if the short-term laws of evolution are known only in a fuzzy form and the information on the initial state of the system is also fuzzy or if we do not have a reasonable statistical model describing the systems environment the tizzy approach is more appropriate. We will show, that the introduction of the fuzzy state, fuzzy velocity and use of the fuzzy logic rules for obtaining the equation of evolution of the system leads to a consistent description of the fuzzy dynamics. Our approach is based on the fuzzy master equation-an analog of the equation describing the Markov process in stochastic dynamics. For continuous evolution we obtain differential equations describing the flows of the fuzzy state. Two cases of "weak and strong fuzziness" are considered. A comparison with other approaches to fuzzy dynamics is performed.

International Conference on System Science and Simulation in Engineering, Dec 16, 2006

Intentional actions may be a consequence of the endogenous compensation of a drop in excitability... more Intentional actions may be a consequence of the endogenous compensation of a drop in excitability after damage induced by a motivational excitation. A neuron does not support factors of its inner environment within the scope of the predetermined standard at the expense of the alteration of other values. The only exception is the level of damage, which neuron tries to decrease by mean of homeostatic compensation. We consider exertion in neuronal metabolism as a driving force, which induces actions directed against actual or anticipated damage. Resulting goaldirected behavior will for a side observer look like an "aspiration to life" and is rather appropriate for description of aware decision-making and fuzzy logic.

Physica D: Nonlinear Phenomena, Apr 1, 2017

h i g h l i g h t s • Dynamic theory of homeostasis based on a generalized Lagrangian approach (S... more h i g h l i g h t s • Dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian). • A living organism, capable of ''feeling distress'' should exhibit homeostasis. • The approach can also be extended to social systems.

ABSTRACT Many theories relate to the brain as a complex network of neurons, which are approximate... more ABSTRACT Many theories relate to the brain as a complex network of neurons, which are approximated as simple elements that make summation of excitations and generate output reaction in accordance with simple activation functions. Such an idealization, however, is far from the properties of a real neuron. In the first part of this paper we present a comprehensive review of the literature and results of the original experiments which supply trustworthy evidence that a real neuron makes a prediction of consequences of input signals and generates an output signal in conformity with this prediction. Based on the experimental data we point out that the phenomenon of motivation appears already on the neuronal level as the phenomenon of avoidance of neuron damage. We argue also that avoidance of injury and aspiration to live is one of the main parts of physiological regulation of the neuron learning and the motivational processes.

Fuzzy Sets and Systems, Jul 1, 2001

In this paper fuzzy dynamics are applied to the description of motivated behavior. We have shown ... more In this paper fuzzy dynamics are applied to the description of motivated behavior. We have shown that in an important case of instrumental reflex elaboration the theory gives a good agreement with the experiment and clears up an important biological and behavioral features of this phenomenon.

h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of... more h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of the system and the dynamics laws. • Evolution of these systems is equivalent to Generalized Lagrangian Mechanics. • Approach does not depend on specific properties of the system and may be equally applied to non-physical systems. • Principal of least action is a consequence of the causality principle and the local topology of the state space.

h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of... more h i g h l i g h t s • Complex system, given non-stochastic imprecise knowledge about the state of the system and the dynamics laws. • Evolution of these systems is equivalent to Generalized Lagrangian Mechanics. • Approach does not depend on specific properties of the system and may be equally applied to non-physical systems. • Principal of least action is a consequence of the causality principle and the local topology of the state space.

Journal of Clinical Oncology, Jun 1, 2023

A new approach to description of the global behavior of a fizzy system with information on short ... more A new approach to description of the global behavior of a fizzy system with information on short term evolution is proposed and investigated. The approach is based on the fuzzy master equation. For continuous evolution the digerential equations describing the flows of the fizzy state w obtained. Two cases of Kweak and strong fizziness" are considered.

Physica D: Nonlinear Phenomena, Jul 1, 2019

In this study, we extended our previous Lagrangian Fuzzy dynamics (S-Lagrangian dynamics) to the ... more In this study, we extended our previous Lagrangian Fuzzy dynamics (S-Lagrangian dynamics) to the systems of fields. Unlike common Lagrangian dynamics, additional "ghost"-fields, which have dual roles, appear in S-Lagrangian dynamics equations. These fields design hierarchical structures of a system and generate "ghost"-forces. In addition, the dynamics of these fields could lead to time irreversibility of the dynamics equations. Because the inference of S-Lagrangian equations is based only the causality principle, the common local topology of a system's state space, and assumptions that infinite velocities are impossible and that the system's state can be described by a compact fuzzy set, S-Lagrangian dynamics can be applied to physical and nonphysical systems as well. We applied S-Lagrangian dynamics to describe the behavior of populations of living species in the environment, assuming that the system's Lagrangian is defined by the dependence of velocity of changing of the population's stress on population densities, food supply, and environmental damage. The results show that even the first approximation of the Lagrangian allows the description of almost all types of species co-evolution: competition, coexistence, prey-predator dynamics, and ecological catastrophes.

Physica D: Nonlinear Phenomena, Nov 1, 2017

 Many-body system with S-dependent Lagrangian inevitably develops a hierarchical structure.  La... more  Many-body system with S-dependent Lagrangian inevitably develops a hierarchical structure.  Lagrangian and energy of these systems are vector functions, while conjugated momenta are second-order tensors.  Dominance hierarchies are determined by differences between individuals in coping with stress.

Social Science Research Network, 2022

Physical Review Letters, Apr 10, 1995

We have developed a theory of a phase transition under pressure in materials made from fibers. Us... more We have developed a theory of a phase transition under pressure in materials made from fibers. Using the path integral technique the free energy of the system is calculated. It is shown that a first order phase transition takes place and that the behavior of the thermodynamic parameters in the ordered phase are in accordance with scaling laws. Experimental data for leather agree qualitatively with the theory.

Physics Letters, Oct 1, 1988

ABSTRACT There exists a large population whose speech is considerably impaired and effectively un... more ABSTRACT There exists a large population whose speech is considerably impaired and effectively unintelligible. This group includes children as well as adults. The lack of successful human communication which they experience is a severe limitation and can even adversely affect their cognitive and social development. The goal of this work is to create a compact and stand alone system for online audio-translation of discrete impaired speech. Such a handy voice-input voice-output communication aid (VIVOCA) does not presently exist on the market. To this end, an appropriate method was developed for handicapped speech recognition. The system consists of two units: one module for recording and preprocessing the handicapped person's speech, based on a PC computer; and a stand alone, portable device for on-line recognition and translation based on a modified neural network. The procedure of translation takes about 0.5 sec., and the testing gives about 90% accuracy

Fuzzy Sets and Systems, Aug 1, 1999

We propose a description of continuous evolution of systems with uncertainty based on min or prod... more We propose a description of continuous evolution of systems with uncertainty based on min or product t-norms of fuzzy logic. We show that the dynamics has a Hamiltonian form in the extended state space composed from "physical" and "information" components if the min t-norm is used. This description is useful when available information on a system behavior is mainly ordinal and not numerical. If the product t-norm is used, the dynamics on a continuous universe is similar to the dynamics of stochastic processes , but the probability distribution is replaced by a possibility density. We show, that such replacement leads to an essential extension of the stochastic process theory. The differential equation of evolution of the possibility density cover most basic dynamics equations in physics.

arXiv (Cornell University), Mar 7, 2022

In this paper we consider generalization of classical/quantum mechanics that directly follows fro... more In this paper we consider generalization of classical/quantum mechanics that directly follows from the causality principle and topology of a system's state space. In generalized mechanics, the Hamiltonian/Schrodinger equations remain the same, but the Hamiltonian may depend on the action and its canonically conjugated variables as additional dynamical variables. This extension of quantum mechanics indicates that the quantization of matter could be an evolutionary process, and in the distant future, even massive bodies may become entirely quantum objects without welldefined trajectories and shapes. In the classical limit, the first approximation of the Hamiltonian with respect to the action explains the accelerated expansion of the Universe, Hubble's law, formation of spiral galaxies with a non-Kepler curve of rotation velocity, and asymmetry between distributions of matter and antimatter. This theory predicts that our open universe could have extended prehistory and be preceded by a long set of closed precursor universes.

International Journal of Biological Macromolecules, Nov 1, 2010

In this paper we propose a theory, which considers the behavior of a circular macromolecule neari... more In this paper we propose a theory, which considers the behavior of a circular macromolecule nearing its transition phase to a condensed state. In particular, the explicit dependence of the phase transition characteristics on the macromolecule's topology is discussed. An important example of a circular macromolecule is bacterial DNA, and although the crystalline state appears incompatible with life, simple organisms use crystallization of DNA for protection against varied environmental assaults. It is shown that the cellular conditions that determine super-helical properties regulate the packaging of DNA as well and, therefore, regulate bacterial endurance and virulence.

Neurocomputing, 1997

... a) Initial state of network is far enough from correlated embedded patterns, (b) initial stat... more ... a) Initial state of network is far enough from correlated embedded patterns, (b) initial state ofnetwork is near ... The dj = a(.(ckj o) y) are linear net gains, 6 = 0((ckj (o) y; (c uo) y) are ... Then for ck, WQ K we can omit the indexes in the linear net gain and saturation coefficients in (8.1). ...

Physica D: Nonlinear Phenomena, Dec 1, 2014

In this paper, we show how to study the evolution of a complex system, given imprecise knowledge ... more In this paper, we show how to study the evolution of a complex system, given imprecise knowledge about the state of the system and the dynamics laws. It will be shown that dynamics of these systems is equivalent to Lagrangian (or Hamiltonian) mechanics in a n+1n+1n+1-dimensional space, where nnn is a system's dimensionality. In some cases, however, the corresponding Lagrangian is more general than the usual one and could depend on the action. In this case, Lagrange's equations gain a non-zero right side proportional to the derivative of the Lagrangian with respect to the action. Examples of such systems are unstable systems, systems with dissipation and systems which can remember their history. Moreover, in certain situations, the Lagrangian could be a set-valued function. The corresponding equations of motion then become differential inclusions instead of differential equations. We will also show that the principal of least action is a consequence of the causality principle and the local topology of the state space and not an independent axiom of classical mechanics.

We emphasize that our adaptation of Lagrangian mechanics does not use or depend on specific properties of the physical system being modeled. Therefore, this Lagrangian approach may be equally applied to \emph{non-physical} systems. An example of such an application is presented as well.

Fuzzy Sets and Systems, Nov 1, 1996

The global behavior of a system with information on fuzzy-described short-term evolution laws is ... more The global behavior of a system with information on fuzzy-described short-term evolution laws is proposed and investigated in the paper. For deterministic or stochastic models such problems are solved by use of differential equations describing the short-term laws. But if the short-term laws of evolution are known only in a fuzzy form and the information on the initial state of the system is also fuzzy or if we do not have a reasonable statistical model describing the systems environment the tizzy approach is more appropriate. We will show, that the introduction of the fuzzy state, fuzzy velocity and use of the fuzzy logic rules for obtaining the equation of evolution of the system leads to a consistent description of the fuzzy dynamics. Our approach is based on the fuzzy master equation-an analog of the equation describing the Markov process in stochastic dynamics. For continuous evolution we obtain differential equations describing the flows of the fuzzy state. Two cases of "weak and strong fuzziness" are considered. A comparison with other approaches to fuzzy dynamics is performed.

International Conference on System Science and Simulation in Engineering, Dec 16, 2006

Intentional actions may be a consequence of the endogenous compensation of a drop in excitability... more Intentional actions may be a consequence of the endogenous compensation of a drop in excitability after damage induced by a motivational excitation. A neuron does not support factors of its inner environment within the scope of the predetermined standard at the expense of the alteration of other values. The only exception is the level of damage, which neuron tries to decrease by mean of homeostatic compensation. We consider exertion in neuronal metabolism as a driving force, which induces actions directed against actual or anticipated damage. Resulting goaldirected behavior will for a side observer look like an "aspiration to life" and is rather appropriate for description of aware decision-making and fuzzy logic.

Physica D: Nonlinear Phenomena, Apr 1, 2017

h i g h l i g h t s • Dynamic theory of homeostasis based on a generalized Lagrangian approach (S... more h i g h l i g h t s • Dynamic theory of homeostasis based on a generalized Lagrangian approach (S-Lagrangian). • A living organism, capable of ''feeling distress'' should exhibit homeostasis. • The approach can also be extended to social systems.

ABSTRACT Many theories relate to the brain as a complex network of neurons, which are approximate... more ABSTRACT Many theories relate to the brain as a complex network of neurons, which are approximated as simple elements that make summation of excitations and generate output reaction in accordance with simple activation functions. Such an idealization, however, is far from the properties of a real neuron. In the first part of this paper we present a comprehensive review of the literature and results of the original experiments which supply trustworthy evidence that a real neuron makes a prediction of consequences of input signals and generates an output signal in conformity with this prediction. Based on the experimental data we point out that the phenomenon of motivation appears already on the neuronal level as the phenomenon of avoidance of neuron damage. We argue also that avoidance of injury and aspiration to live is one of the main parts of physiological regulation of the neuron learning and the motivational processes.

Fuzzy Sets and Systems, Jul 1, 2001

In this paper fuzzy dynamics are applied to the description of motivated behavior. We have shown ... more In this paper fuzzy dynamics are applied to the description of motivated behavior. We have shown that in an important case of instrumental reflex elaboration the theory gives a good agreement with the experiment and clears up an important biological and behavioral features of this phenomenon.

In this paper we propose a theory, which considers the behavior of a circular macromolecule neari... more In this paper we propose a theory, which considers the behavior of a circular
macromolecule nearing its transition phase to a condensed state. In
particular, the explicit dependence of the phase transition characteristics on
the macromolecule's topology is discussed. An important example of a circular
macromolecule is bacterial DNA, and although the crystalline state appears incompatible
with life, simple organisms use crystallization of DNA for protection against varied
environmental assaults. It is shown that the cellular conditions that determine
super-helical properties regulate the packaging of DNA as well
and, therefore, regulate bacterial endurance and virulence.