Discrete Internal States Research Articles

Putting it into words: Emotion vocabulary, emotion differentiation, and depression among adolescents.

Emotion differentiation (ED; the ability to distinguish discrete internal emotion states) may reflect or benefit from knowledge of linguistic labels. The present study uses natural language processing to examine how emotion vocabulary (EV; diversity of unique emotion terms within active vocabulary) relates to ED and depression in an adolescent sample. We tested two competing preregistered (https://osf.io/4j75w/) models regarding the EV-ED link. In the lexical facilitation hypothesis, we posited that larger EV may inform ED, perhaps resulting in larger EVs being associated with greater ED. In the emotional concision hypothesis, we theorized that ED may reflect narrower emotional experiences that are more succinctly labelled, which could result in larger EV being associated with lower ED. A community sample of adolescents (N = 241, ages 14-17, predominantly White) completed interviews, self-report measures, and ecological momentary assessments as part of a larger study conducted between 2014 and 2016. EV was derived using speech samples from transcribed recordings of life stress interviews. In line with the emotion concision hypothesis, EV and ED were inversely related for negative emotions. Moreover, larger negative EV and lower negative ED were each uniquely associated with depression, casting further doubt on whether diverse negative EVs within spontaneous language are fundamentally adaptive for emotional functioning. Replication in more diverse samples is needed to extend generalizability. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Truncated stochastically switching processes.

There are a large variety of hybrid stochastic systems that couple a continuous process with some form of stochastic switching mechanism. In many cases the system switches between different discrete internal states according to a finite-state Markov chain, and the continuous dynamics depends on the current internal state. The resulting hybrid stochastic differential equation(hSDE) could describe the evolution of a neuron's membrane potential, the concentration of proteins synthesized by a gene network, or the position of an active particle. Another major class of switching system is a search process with stochastic resetting, where the position of a diffusing or active particle is reset to a fixed position at a random sequence of times. In this case the system switches between a search phase and a reset phase, where the latter may be instantaneous. In this paper, we investigate how the behavior of a stochastically switching system is modified when the maximum number of switching (or reset) events in a given time interval is fixed. This is motivated by the idea that each time the system switches there is an additive energy cost. We first show that in the case of an hSDE, restricting the number of switching events is equivalent to truncating a Volterra series expansion of the particle propagator. Such a truncation significantly modifies the moments of the resulting renormalized propagator. We then investigate how restricting the number of reset events affects the diffusive search for an absorbing target. In particular, truncating a Volterra series expansion of the survival probability, we calculate the splitting probabilities and conditional MFPTs for the particle to be absorbed by the target or exceed a given number of resets, respectively.

Cooperativity, Information Gain, and Energy Cost During Early LTP in Dendritic Spines.

We investigate a mutual relationship between information and energy during the early phase of LTP induction and maintenance in a large-scale system of mutually coupled dendritic spines, with discrete internal states and probabilistic dynamics, within the framework of nonequilibrium stochastic thermodynamics. In order to analyze this computationally intractable stochastic multidimensional system, we introduce a pair approximation, which allows us to reduce the spine dynamics into a lower-dimensional manageable system of closed equations. We found that the rates of information gain and energy attain their maximal values during an initial period of LTP (i.e., during stimulation), and after that, they recover to their baseline low values, as opposed to a memory trace that lasts much longer. This suggests that the learning phase is much more energy demanding than the memory phase. We show that positive correlations between neighboring spines increase both a duration of memory trace and energy cost during LTP, but the memory time per invested energy increases dramatically for very strong, positive synaptic cooperativity, suggesting a beneficial role of synaptic clustering on memory duration. In contrast, information gain after LTP is the largest for negative correlations, and energy efficiency of that information generally declines with increasing synaptic cooperativity. We also find that dendritic spines can use sparse representations for encoding long-term information, as both energetic and structural efficiencies of retained information and its lifetime exhibit maxima for low fractions of stimulated synapses during LTP. Moreover, we find that such efficiencies drop significantly with increasing the number of spines. In general, our stochastic thermodynamics approach provides a unifying framework for studying, from first principles, information encoding, and its energy cost during learning and memory in stochastic systems of interacting synapses.

Stability and [formula omitted] performance of human-in-the-loop control systems through hidden semi-Markov human behavior modeling

In this paper, a stochastic framework of analysis and synthesis is proposed for the stability and H∞ performance of linear human-in-the-loop (HiTL) control systems which involve both human’s discrete internal states and machine’s continuous-time dynamics. Initially, a hidden semi-Markov model (HS-MM) is used for the human behavior modeling, which takes into account the random nature of human internal state (HIS) reasoning and the sojourn time of HIS, as well as the uncertainty from HIS observation. Subsequently, by integrating human model, machine model, and their interaction, a hidden semi-Markov jump system (HS-MJS) model is constructed to describe the HiTL control system. By the tools of stochastic Lyapunov functional and linear matrix inequalities (LMIs), a sufficient and necessary condition for the stochastic stability of the HiTL control system via state feedback is then given on the basis of the HS-MJS model. Besides, an LMI-based human-assistance stabilizing control design is developed. For the prescribed disturbance attenuation level, a human-assistance H∞ controller synthesis method of the HiTL control system is proposed in terms of LMIs. Finally, the developed theoretical results are applied to the steering control of the lane-keeping assistance system.

EXAMPLES OF INFORMATION TECHNOLOGIES FOR RECONSTRUCTION FROM THE DATA OF THE SPECTRUM OF SOME CLASSES OF RANDOM FUNCTIONS

It is known that a stationary random process is represented as a superposition of harmonic oscillations with real frequencies and uncorrelated amplitudes. In the study of nonstationary processes, it is natural to have increasing or declining oscillationсs. This raises the problem of constructing algorithms that would allow constructing broad classes of nonstationary processes from elementary nonstationary random processes. A natural generalization of the concept of the spectrum of a nonstationary random process is the transition from the real spectrum in the case of stationary to a complex or infinite multiple spectrum in the nonstationary case. There is also the problem of describing within the correlation theory of random processes in which the spectrum has no analogues in the case of stationary random processes, namely, the spectrum point is real, but it has infinite multiplicity for the operator image of the corresponding operator, and when the spectrum itself is complex. Reconstruction of the complex spectrum of a nonstationary random function is a very important problem in both theoretical and applied aspects. In the paper the procedure of reconstruction of random process, sequence, field from a spectrum for Gaussian random functions is developed. Compared to the stationary case, there are wider possibilities, for example, the construction of a nonstationary random process with a real spectrum, which has infinite multiplicity and which can be distributed over the entire finite segment of the real axis. The presence of such a spectrum leads, in contrast to the case of a stationary random process, to the appearance of new components in the spectral decomposition of random functions that correspond to the internal states of "strings", i.e. generated by solutions of systems of equations in partial derivatives of hyperbolic type. The paper deals with various cases of the spectrum of a non-self-adjoint operator A, namely, the case of a discrete spectrum and the case of a continuous spectrum, which is located on a finite segment of the real axis, which is the range of values of the real non-decreasing function a (x). The cases a (x) = 0, a (x) = const, a (x) = x and a (x) is a piecewise constant function are studied. The authors consider the recovery of nonstationary sequences for different cases of the spectrum of a non-self-adjoint operator A promising since spectral decompositions are a superposition of discrete or continuous internal states of oscillators with complex frequencies and uncorrelated amplitudes and therefore have deep physical meaning.

RECONSTRUCTION OF GAUSSIAN RANDOM FUNCTIONS FROM SPECTRUM DATA

It is known that a stationary random process is represented as a superposition of harmonic oscillations with real frequencies and uncorrelated amplitudes. In the study of nonstationary processes, it is natural to have increasing or declining oscillationсs. This raises the problem of constructing algorithms that would allow constructing broad classes of nonstationary processes from elementary nonstationary random processes. A natural generalization of the concept of the spectrum of a nonstationary random process is the transition from the real spectrum in the case of stationary to a complex or infinite multiple spectrum in the nonstationary case. There is also the problem of describing within the correlation theory of random processes in which the spectrum has no analogues in the case of stationary random processes, namely, the spectrum point is real, but it has infinite multiplicity for the operator image of the corresponding operator, and when the spectrum itself is complex. Reconstruction of the complex spectrum of a nonstationary random function is a very important problem in both theoretical and applied aspects. In the paper the procedure of reconstruction of random process, sequence, field from a spectrum for Gaussian random functions is developed. Compared to the stationary case, there are wider possibilities, for example, the construction of a nonstationary random process with a real spectrum, which has infinite multiplicity and which can be distributed over the entire finite segment of the real axis. The presence of such a spectrum leads, in contrast to the case of a stationary random process, to the appearance of new components in the spectral decomposition of random functions that correspond to the internal states of «strings», i.e. generated by solutions of systems of equations in partial derivatives of hyperbolic type. The paper deals with various cases of the spectrum of a non-self-adjoint operator , namely, the case of a discrete spectrum and the case of a continuous spectrum, which is located on a finite segment of the real axis, which is the range of values of the real non-decreasing function a(x). The cases a(x)=0, a(x)=a0, a(x)=x and a(x) is a piecewise constant function are studied. The authors consider the recovery of nonstationary sequences for different cases of the spectrum of a non-self-adjoint operator promising since spectral decompositions are a superposition of discrete or continuous internal states of oscillators with complex frequencies and uncorrelated amplitudes and therefore have deep physical meaning.

The Difficulty of Learning Long-Term Dependencies with Gradient Flow in Recurrent Nets

In theory, recurrent networks (RN) can leverage their feedback connections to store activations as representations of recent input events. The most extensively used methods for learning what to put in short-term memory, on the other hand, take far too long to be practicable or do not work at all, especially when the time lags between inputs and instructor signals are long. They do not provide significant practical advantages over, the backdrop in feedforward networks with limited time windows, despite being theoretically fascinating. The goal of this article is to have a succinct overview of this rapidly evolving topic, with a focus on recent advancements. Also, we examine the asymptotic behavior of error gradients as a function of time lags to provide a hypothetical treatment of this topic. The methodology adopted in the study was to review some scholarly research papers on the subject matter to address the difficulty of learning long-term dependencies with gradient flow in recurrent nets. RNNs are the most general and powerful sequence learning algorithm currently available. Unlike Hidden Markov Models (HMMs), which have proven to be the most successful technique in a variety of sequence processing applications, they are not limited to discrete internal states and can represent continuous, dispersed sequences. As a result, they can address problems that no other method can. Conventional RNNs, on the other hand, are difficult to train due to the problem of vanishing gradients.

Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System.

The hybrid approach to quantum computation simultaneously utilizes both discrete and continuous variables, which offers the advantage of higher density encoding and processing powers for the same physical resources. Trapped ions, with discrete internal states and motional modes that can be described by continuous variables in an infinite-dimensional Hilbert space, offer a natural platform for this approach. A nonlinear gate for universal quantum computing can be implemented with the conditional beam splitter Hamiltonian |e⟩⟨e|(a[over ^]^{†}b[over ^]+a[over ^]b[over ^]^{†}) that swaps the quantum states of two motional modes, depending on the ion's internal state. We realize such a gate and demonstrate its applications for quantum state overlap measurements, single-shot parity measurement, and generation of NOON states.

Exact stationary state of a run-and-tumble particle with three internal states in a harmonic trap

We study the motion of a one-dimensional run-and-tumble particle with three discrete internal states in the presence of a harmonic trap of stiffness The three internal states, corresponding to positive, negative and zero velocities respectively, evolve following a jump process with rate . We compute the stationary position distribution exactly for arbitrary values of and which turns out to have a finite support on the real line. We show that the distribution undergoes a shape-transition as is changed. For the distribution has a double-concave shape and shows algebraic divergences with an exponent both at the origin and at the boundaries. For the position distribution becomes convex, vanishing at the boundaries and with a single, finite, peak at the origin. We also show that for the special case the distribution shows a logarithmic divergence near the origin while saturating to a constant value at the boundaries.

Familiarity, recollection, and receiver-operating characteristic (ROC) curves in recognition memory.

The Atkinson-Shiffrin theory describes and explains some of the processes involved in storing and retrieving information in human memory. Here we examine predictions of related models for search and decision processes in recognizing information in long-term memory. In some models, recognition is presumably based on a test item's familiarity judgment, and subsequent decisions follow from the sensitivity and decision parameters of signal detection theory. Other models dispense with the continuous notion of familiarity and base recognition on discrete internal states such as relative certainty that an item has or has not been previously studied, with an intermediate state of uncertainty that produces guesses. Still others are hybrid models with two criteria located along a familiarity continuum defining areas for rapid decisions based on high or low familiarities. For intermediate familiarity values, the decision can be delayed pending the results of search for, and occasional recollection of, relevant episodic information. Here we present the results from a study of human recognition memory for lists of words using both response time and error data to construct receiver-operating characteristic (ROC) curves derived from three standard methods based on the same data set. Models are evaluated against, and parameters estimated from, group as well as individual subjects' behavior. We report substantially different ROC curves when they are based on variations in target-word frequency, confidence judgments, and response latencies. The results indicate that individual versus group data must be used with caution in determining the appropriate theoretical interpretation of recognition memory performance.

Identification of Complex Production Systems with Using Iterative Networks

In the article the technique of identification of complex production systems using iterative networks is considered. The identification process begins with the allocation of functional blocks, which can later be described by automata working with discrete information and changing internal states only at specified times. The basic laws of the functioning of the selected subsystems are simulated. Characteristics of cells formed parameters associated with multi-step manufacturing process. As the semi-finished product passes through the processing stages under consideration, the values of the technological factors being realized are fixed in the system being formed.

Vibrations of an Euler-Bernoulli beam with hysteretic damping arising from dispersed frictional microcracks

We study free and harmonically forced vibrations of an Euler-Bernoulli beam with rate-independent hysteretic dissipation. The dissipation follows a model proposed elsewhere for materials with randomly dispersed frictional microcracks. The virtual work of distributed dissipative moments is approximated using Gaussian quadrature, yielding a few discrete internal hysteretic states. Lagrange's equations are obtained for the modal coordinates. Differential equations for the modal coordinates and internal states are integrated together. Free vibrations decay exponentially when a single mode dominates. With multiple modes active, higher modes initially decay rapidly while lower modes decay relatively slowly. Subsequently, lower modes show their own characteristic modal damping, while small amplitude higher modes show more erratic decay. Large dissipation, for the adopted model, leads mathematically to fast and damped oscillations in the limit, unlike viscously overdamped systems. Next, harmonically forced, lightly damped responses of the beam are studied using both a slow frequency sweep and a shooting-method based search for periodic solutions along with numerical continuation. Shooting method and frequency sweep results match for large ranges of frequency. The shooting method struggles near resonances, where internal states collapse into lower dimensional behavior and Newton-Raphson iterations fail. Near the primary resonances, simple numerically-aided harmonic balance gives excellent results. Insights are also obtained into the harmonic content of secondary resonances.

Steady diffusion in a drift field: A comparison of large-deviation techniques and multiple-scale analysis.

A particle with internal unobserved states diffusing in a force field will generally display effective advection-diffusion. The drift velocity is proportional to the mobility averaged over the internal states, or effective mobility, while the effective diffusion has two terms. One is of the equilibrium type and satisfies an Einstein relation with the effective mobility while the other is quadratic in the applied force. In this contribution we present two new methods to obtain these results, on the one hand using large deviation techniques and on the other by a multiple-scale analysis, and compare the two. We consider both systems with discrete internal states and continuous internal states. We show that the auxiliary equations in the multiple-scale analysis can also be derived in second-order perturbation theory in a large deviation theory of a generating function (discrete internal states) or generating functional (continuous internal states). We discuss that measuring the two components of the effective diffusion give a way to determine kinetic rates from only first and second moments of the displacement in steady state.

The Theory of Ultra-Coarse-Graining. 3. Coarse-Grained Sites with Rapid Local Equilibrium of Internal States.

When viewed through a coarse-grained lens, important molecular and biophysical systems can appear to undergo discrete, switch-like state changes in addition to more continuous configurational motions. One of our recent papers described a theory for bottom-up coarse-graining of the equilibrium statistics of models with such behavior, called ultra-coarse-grained (UCG) models, and a follow up paper described an implementation when the states of the coarse-grained sites or "beads" change rarely. However, not all systems with this discrete behavior fall under that special limit. This article develops the general UCG theory for the opposite limit, that is, where the internal states of the CG particles or beads adjust rapidly so as to always remain effectively at quasi-equilibrium no matter what the positions of the coarse-grained particles. This rapid local equilibrium allows ultra-coarse-graining to mix standard coarse-grained force fields by using local order parameters to control the degree of mixing, which adds an environmental dependence and many-body effects to the coarse-grained model while requiring minimal new coding. This article first presents the definition of such UCG force fields as well as their fitting procedures from atomistic-scale data, and then it presents three examples of UCG simulations with an approach that we call UCG with rapid local equilibrium (UCG-RLE). We then present an application of UCG-RLE using the full bottom-up methodology to coarse-grain and simulate cooperative hydrophobic association of neopentane in methanol solvent. UCG-RLE force matching does a superior job of matching solute-solute correlation functions and solute cluster size distributions compared to the more standard force-matched models not having coarse-grained sites with discrete internal states.

Development of a model representing systems protected against research*

The research described herein presents a method of modeling information systems with dynamic parameters. The model includes elements with discrete internal states and agents, which can act in the system by modifying states of the system’s elements. The research has two objectives aimed at protection against research, which are as follows: inadmissibility for the system to transfer into some specific states and invisibility of actions taken by the agents. The present paper establishes stable secure states and proves algorithmic insolubility of Problem 1 in its general case.

A biophysical model of cell evolution after cytotoxic treatments: Damage, repair and cell response

We present a theoretical agent-based model of cell evolution under the action of cytotoxic treatments, such as radiotherapy or chemotherapy. The major features of cell cycle and proliferation, cell damage and repair, and chemical diffusion are included. Cell evolution is based on a discrete Markov chain, with cells stepping along a sequence of discrete internal states from ‘normal’ to ‘inactive’. Probabilistic laws are introduced for each type of event a cell can undergo during its life: duplication, arrest, senescence, damage, reparation, or death. We adjust the model parameters on a series of cell irradiation experiments, carried out in a clinical LINAC, in which the damage and repair kinetics of single- and double-strand breaks are followed. Two showcase applications of the model are then presented. In the first one, we reconstruct the cell survival curves from a number of published low- and high-dose irradiation experiments. We reobtain a very good description of the data without assuming the well-known linear-quadratic model, but instead including a variable DSB repair probability. The repair capability of the model spontaneously saturates to an exponential decay at increasingly high doses. As a second test, we attempt to simulate the two extreme possibilities of the so-called ‘bystander’ effect in radiotherapy: the ‘local’ effect versus a ‘global’ effect, respectively activated by the short-range or long-range diffusion of some factor, presumably secreted by the irradiated cells. Even with an oversimplified simulation, we could demonstrate a sizeable difference in the proliferation rate of non-irradiated cells, the proliferation acceleration being much larger for the global than the local effect, for relatively small fractions of irradiated cells in the colony.

Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity

We study spatial correlations in the ground state of a one-dimensional electron gas coupled to a dynamic quantum impurity. The system displays a nontrivial many-body effect known as the Fermi edge singularity: transitions between discrete internal states of the impurity have a power-law dependence on the internal energies of the impurity states. We present compact formulas for the static current-current correlator and the pair-correlation function. These reveal that spatial correlations induced by the impurity decay slowly (as the third inverse power of distance) and have a power-law energy dependence, characteristic of the Fermi edge singularity.

Serial interspike interval correlations of excitable neurons with memory

Many theoretical studies of spiking neurons rely on thesimplifying renewal assumption, meaning that interspikeintervals (ISIs) of a spike train are statistically independ-ent. Experimental measurements of serial ISI correlationshave revealed, however, that the renewal assumption isviolated in various systems. For instance, strong but short-lived, negative correlations have been reported for P-unitsof weakly electric fish [1,2] and for pyramidal neurons inrat entorhinal cortex [3]. For a review, see [4]. Positive cor-relations that extend over many ISIs have been observedin [5]. Neurons exhibiting spike-frequency adaptationtypically display negative serial correlations, whereas slowinput variations typically induce positive serial correla-tions [6].Theoretical work has gained much insight into the benefi-cial role of serial correlations for signal transmission [7].In that case, the calculation of the serial correlation coef-ficient (SCC) could be accomplished by the use of a par-ticularly simple neuron model that operates in theoscillatory regime and features a dynamic firing threshold.In general, however, the SCC is difficult to access analyti-cally, which is due to the non-Markovian nature of non-renewal neuron models. Here, we present a novel tech-nique that allows us to calculate the SCC of a large class ofnon-renewal neurons operating in the excitable regime.Specifically, we consider neurons with discrete internalstates or discrete states of the external driving function.The analytical approach is based on a generalization ofthe discrete kinetic scheme used to investigate residencetime correlations in driven bistable systems [8,9].Having established the general method to obtain the SCCfor arbitrary lags between ISIs, we consider two specialcases that are of particular interest. The first case mimics aleaky integrate-and-fire (LIF) neuron with dynamicthreshold, which has been proposed as a model for spike-frequency adaptation. By discretizing the threshold intothree states, we find a negative SCC at lag one and vanish-ing correlations at higher lags. In the second case, we con-sider a neuron that participates in a network that switchesbetween Up and Down states. The theory reveals positiveserial correlations that decay exponentially with the lag.Interestingly, for slow two-state synaptic input the SCC atlag one is maximized at an optimal amplitude of the two-state driving. Our theoretical expressions agree well withextensive simulations of noisy LIF neurons. Finally wemention, that an analytical formula for the SCC could beuseful to model measured data by tuning the parametersof the discrete neuron model.

Self-replicating machines in continuous space with virtual physics.

JohnnyVon is an implementation of self-replicating machines in continuous two-dimensional space. Two types of particles drift about in a virtual liquid. The particles are automata with discrete internal states but continuous external relationships. Their internal states are governed by finite state machines, but their external relationships are governed by a simulated physics that includes Brownian motion, viscosity, and springlike attractive and repulsive forces. The particles can be assembled into patterns that can encode arbitrary strings of bits. We demonstrate that, if an arbitrary seed pattern is put in a soup of separate individual particles, the pattern will replicate by assembling the individual particles into copies of itself. We also show that, given sufficient time, a soup of separate individual particles will eventually spontaneously form self-replicating patterns. We discuss the implications of JohnnyVon for research in nanotechnology, theoretical biology, and artificial life.

Real-time computing without stable states: a new framework for neural computation based on perturbations.

A key challenge for neural modeling is to explain how a continuous stream of multimodal input from a rapidly changing environment can be processed by stereotypical recurrent circuits of integrate-and-fire neurons in real time. We propose a new computational model for real-time computing on time-varying input that provides an alternative to paradigms based on Turing machines or attractor neural networks. It does not require a task-dependent construction of neural circuits. Instead, it is based on principles of high-dimensional dynamical systems in combination with statistical learning theory and can be implemented on generic evolved or found recurrent circuitry. It is shown that the inherent transient dynamics of the high-dimensional dynamical system formed by a sufficiently large and heterogeneous neural circuit may serve as universal analog fading memory. Readout neurons can learn to extract in real time from the current state of such recurrent neural circuit information about current and past inputs that may be needed for diverse tasks. Stable internal states are not required for giving a stable output, since transient internal states can be transformed by readout neurons into stable target outputs due to the high dimensionality of the dynamical system. Our approach is based on a rigorous computational model, the liquid state machine, that, unlike Turing machines, does not require sequential transitions between well-defined discrete internal states. It is supported, as the Turing machine is, by rigorous mathematical results that predict universal computational power under idealized conditions, but for the biologically more realistic scenario of real-time processing of time-varying inputs. Our approach provides new perspectives for the interpretation of neural coding, the design of experiments and data analysis in neurophysiology, and the solution of problems in robotics and neurotechnology.