analysis of anisotropic sector with a radial crack under anti plane shear loading in this paper the anti plane shear deformation of an anisotropic sector with a radial crack is investigated the traction traction boundary conditions are imposed on the radial edges and the traction free condition is considered on the circular segment of the sector a novel mathematical technique is employed for the solution of the problem this technique consists of the use of some recently proposed finite complex transforms shahani 1999 which have complex analogies to the standard finite mellin transforms of the first and second kinds however it is essential to state the traction free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method the resultant dual integral equations are solved numerically to determine the stress intensity factors at the crack tips in the special cases the obtained results coincide with those cited in the literature

presence of quantum correlations results in a nonvanishing ergotropic gap the paradigm of extracting work from an isolated quantum system through a cyclic hamiltonian process is a topic of immense research interest the optimal work extracted under such a process is termed ergotropy europhys lett 67 565 2004 here in a multiparty scenario we consider only a class of such cyclic processes that can be implemented locally giving rise to the concept of local ergotropy eventually the presence of quantum correlations results in a nonvanishing thermodynamic quantity called an ergotropic gap measured by the difference between global and local ergotropy however the converse does not hold in general i e its nonzero value does not necessarily imply the presence of quantum correlations for arbitrary multiparty states we quantify this gap we also evaluate the difference between maximum global and local extractable work for arbitrary states when the system is no longer isolated but put in contact with a bath of the same local temperature

a new method for complete stability analysis of cellular neural networks with time delay this paper presents new complete stability results for delayed cellular neural networks dcnns a novel method is proposed for complete stability analysis of dcnns by applying the m matrix theory and introducing some new estimation techniques on the solutions of dcnns a simple and improved complete stability criterion is derived the new criterion unifies the delay dependent and delay independent complete stability conditions for dcnns moreover the obtained delay dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained numerical examples are presented which show that the new complete stability results for dcnns are compared favorably with the existing results

permitted and forbidden sets in discrete time linear threshold recurrent neural networks the concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks such concepts exhibit interesting dynamics in recurrent neural networks this paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete time recurrent neural networks the linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations networks in discrete time can directly provide algorithms for efficient implementation in digital hardware the main contribution of this paper is to establish foundations of permitted and forbidden sets necessary and sufficient conditions for the linear threshold discrete time recurrent neural networks are obtained for complete convergence existence of permitted and forbidden sets as well as conditionally multiattractivity respectively simulation studies explore some possible interesting practical applications

an improved global asymptotic stability criterion for delayed cellular neural networks a new lyapunov krasovskii functional is constructed for delayed cellular neural networks and the s procedure is employed to handle the nonlinearities an improved global asymptotic stability criterion is also derived that is a generalization of and an improvement over previous results numerical examples demonstrate the effectiveness of the criterion

analysis of an isotropic finite wedge under antiplane deformation the antiplane deformation of an isotropic wedge with finite radius is studied in this paper depending upon the boundary data prescribed on the circular segment of the wedge traction or displacement two problems are analysed in each problem three different cases of boundary conditions on the radial edges are considered the radial boundary data are traction displacement displacement displacement and traction traction the solution of governing differential equations is accomplished by means of finite mellin transforms the closed form solutions are obtained for displacement and stress fields in the entire domain the geometric singularities of stress fields are identical to those cited in the literature however in displacement displacement case under certain representation of boundary condition another type of singularity has been observed

new stability results for delayed neural networks this paper is concerned with the stability for delayed neural networks by more fully making use of the information of the activation function a new lyapunov krasovskii functional lkf is constructed then a new integral inequality is developed and more information of the activation function is taken into account when the derivative of the lkf is estimated by lyapunov stability theory a new stability result is obtained finally three examples are given to illustrate the stability result is less conservative than some recently reported ones

images in quantum entanglement a system for classifying and quantifying entanglement in spin 1 2 pure states is presented based on simple images from the image point of view an entangled state can be described as a linear superposition of separable object wavefunction o plus a portion of its own inverse image bell states can be defined in this way using the method of images the three spin 1 2 system is discussed in some detail this system can exhibit exclusive three particle 123 entanglement two particle entanglements 12 13 23 and or mixtures of all four all four image states are orthogonal both to each other and to the object wavefunction in general five entanglement parameters 12 13 23 123 and 123 are required to define the general entangled state in addition it is shown that there is considerable scope for encoding numbers at least from the classical point of view but using quantum mechanical principles methods are developed for their extraction it is shown that concurrence can be used to extract even partite but not odd partite information additional relationships are also presented which can be helpful in the decoding process however in general numerical methods are mandatory a simple roulette method for decoding is presented and discussed but it is shown that if the encoder chooses to use transcendental numbers for the angles defining the target function 1 1 etc the method rapidly turns into the devil s roulette requiring finer and finer angular steps

some problems in the antiplane shear deformation of bi material wedges abstract the antiplane shear deformation of a bi material wedge with finite radius is studied in this paper depending upon the boundary condition prescribed on the circular segment of the wedge traction or displacement two problems are analyzed in each problem two different cases of boundary conditions on the radial edges of the composite wedge are considered the radial boundary data are traction displacement and traction traction the solution of governing differential equations is accomplished by means of finite mellin transforms the closed form solutions are obtained for displacement and stress fields in the entire domain the geometric singularities of stress fields are observed to be dependent on material property in general however in the special case of equal apex angles in the traction traction problem this dependency ceases to exist and the geometric singularity shows dependency only upon the apex angle a result which is in agreement with that cited in the literature for bi material wedges with infinite radii in part ii of the paper antiplane shear deformation of bi material circular media containing an interfacial edge crack is considered as a special case of bi material wedges studied in part i of the paper explicit expressions are derived for the stress intensity factor at the tip of an edge crack lying at the interface of the bi material media it is seen that in general the stress intensity factor is a function of material property however in special cases of traction traction problem i e similar materials and also equal apex angles the stress intensity factor becomes independent of material property and the result coincides with the results in the literature

the second laws of quantum thermodynamics the second law of thermodynamics places constraints on state transformations it applies to systems composed of many particles however we are seeing that one can formulate laws of thermodynamics when only a small number of particles are interacting with a heat bath is there a second law of thermodynamics in this regime here we find that for processes which are approximately cyclic the second law for microscopic systems takes on a different form compared to the macroscopic scale imposing not just one constraint on state transformations but an entire family of constraints we find a family of free energies which generalize the traditional one and show that they can never increase the ordinary second law relates to one of these with the remainder imposing additional constraints on thermodynamic transitions we find three regimes which determine which family of second laws govern state transitions depending on how cyclic the process is in one regime one can cause an apparent violation of the usual second law through a process of embezzling work from a large system which remains arbitrarily close to its original state these second laws are relevant for small systems and also apply to individual macroscopic systems interacting via long range interactions by making precise the definition of thermal operations the laws of thermodynamics are unified in this framework with the first law defining the class of operations the zeroth law emerging as an equivalence relation between thermal states and the remaining laws being monotonicity of our generalized free energies

on the almost periodic solution of cellular neural networks with distributed delays by exponential dichotomy about differential equations a formal almost periodic solution aps of a class of cellular neural networks cnns with distributed delays is obtained then within different normed spaces several sufficient conditions guaranteeing the existence and uniqueness of an aps are proposed using two fixed point theorems based on the continuity property and some inequality techniques two theorems insuring the global stability of the unique aps are given comparing with known literatures all conclusions are drawn with slacker restrictions e g do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one and the activation functions to be bounded etc besides all criteria are obtained by different ways finally two illustrative examples show the validity and that all criteria are easy to check and apply

delay dependent stability criteria for generalized neural networks with two delay components this paper investigates the delay dependent stability for generalized continuous neural networks with time varying delays a novel lyapunov krasovskii functional lkf that considers more information on activation functions of delayed neural networks and delay upper bounds is developed simultaneously most commonly used techniques for treating the derivative of the lkf are reviewed and compared with each other with the way of introducing slack matrices those techniques are classified into two categories including free weighting matrix fwm based techniques and reciprocally convex combination based techniques it is found that the introduced slack matrices play an important role in conservatism reducing and those four types of fwm based methods lead to same results and are equivalent moreover the obtained criteria are extended to the system with a single time varying delay two numerical examples are given to verify the effectiveness of the proposed method

a report on the nonlinear squeezed states and their non classical properties of a generalized isotonic oscillator we construct nonlinear squeezed states of a generalized isotonic oscillator potential we demonstrate the non existence of a dual counterpart of nonlinear squeezed states in this system we investigate the statistical properties exhibited by the squeezed states in particular mandel s parameter second order correlation function photon number distributions and parameter a3 in detail we also examine the quadrature and amplitude squared squeezing effects finally we derive the expression for the s parameterized quasi probability distribution function of these states all this information about the system is new to the literature

passivity complete passivity and virtual temperatures we give a simple and intuitive proof that the only states which are completely passive i e those states from which work cannot be extracted even with infinitely many copies are gibbs states at positive temperatures the proof makes use of the idea of virtual temperatures i e the association of temperatures to pairs of energy levels transitions we show that 1 passive states are those where every transition is at a positive temperature and 2 completely passive states are those where every transition is at the same positive temperature

optimal eavesdropping on quantum key distribution without quantum memory we consider the security of the bb84 bennett and brassard 1984 proc ieee int conf on computers systems and signal processing pp 175 9 six state brus 1998 phys rev lett http dx doi org 10 1103 physrevlett 81 3018 and sarg04 scarani et al 2004 phys rev lett http dx doi org 10 1103 physrevlett 92 057901 quantum key distribution protocols when the eavesdropper does not have access to a quantum memory in this case eve s most general strategy is to measure her ancilla with an appropriate positive operator valued measure designed to take advantage of the post measurement information that will be released during the sifting phase of the protocol after an optimization on all the parameters accessible to eve our method provides us with new bounds for the security of six state and sarg04 against a memoryless adversary in particular for the six state protocol we show that the maximum quantum bit error ratio for which a secure key can be extracted is increased from 12 6 for collective attacks to 20 4 with the memoryless assumption

global asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

multistability and new attraction basins of almost periodic solutions of delayed neural networks in this paper we investigate multistability of almost periodic solutions of recurrently connected neural networks with delays simply called delayed neural networks we will reveal that under some conditions the space rn can be divided into 2n subsets and in each subset the delayed n neuron neural network has a locally stable almost periodic solution furthermore we also investigate the attraction basins of these almost periodic solutions we reveal that the attraction basin of almost periodic trajectory is larger than the subset where the corresponding almost periodic trajectory is located in addition several numerical simulations are presented to corroborate the theoretical results

circular quantum secret sharing a circular quantum secret sharing protocol is proposed which is useful and efficient when one of the parties of secret sharing is remote to the others who are in adjacent especially the parties are more than three we describe the process of this protocol and discuss its security when the quantum information carrying is polarized single photons running circularly it will be shown that entanglement is not necessary for quantum secret sharing moreover the theoretic efficiency is improved to approach 100 as almost all the instances can be used for generating the private key and each photon can carry one bit of information without quantum storage it is straightforwardly to utilize this topological structure to complete quantum secret sharing with multi level two particle entanglement in high capacity securely

a bipartite separable ball and its applications in this paper based on a matrix norm we first present a ball of separable un normalized states around the identity matrix for the bipartite quantum system which is larger than the separable ball in frobenius norm then the proposed ball is used to get not only simple sufficient conditions for the separability of pseudopure states and the states with strong positive partial transposes but also a separable ball centered at the identity matrix for the multipartite quantum system

coherent states even and odd coherent states in a finite dimensional hilbert space and their properties we have considered a harmonic oscillator in a finite dimensional hilbert space spanned by orthogonal polynomials of a discrete variable and constructed coherent states as well as even and odd coherent states of this oscillator various properties such as squeezing and antibunching of these states have also been examined

entropy of a subalgebra and quantum estimation in this paper we compare the accessible information of quantum communication channels with the entropic content of finite dimensional matrix algebras with respect to quantum states as defined by connes narnhofer and thirring in particular every abelian n n matrix algebra together with a density matrix define the input alphabet of a quantum communication channel whose accessible information equals the entropic content of the algebra with respect to the state the cases n 2 and n 3 are concretely examined in connection with the problem of the best estimation

an efficient two party quantum private comparison protocol with decoy photons and two photon entanglement following some ideas of the quantum secret sharing qss protocol 2008 phys lett a 372 1957 we propose an efficient quantum private comparison qpc protocol for comparing information of equality with the help of a third party tp the protocol can ensure fairness efficiency and security the protocol is fair which means that one party knows the sound result of the comparison if and only if the other one knows the result the protocol is efficient with the help of the tp for calculating however the tp cannot learn any information about the players respective private inputs and even about the comparison result and cannot collude with any player the protocol is secure for the two players that is any information about their respective secret inputs will not leak except the final computation result a precise proof of security of the protocol is presented applications of this protocol may include private bidding and auctions secret ballot elections commercial business identification in a number of scenarios and so on

how to share a quantum secret we investigate the concept of quantum secret sharing in a k n threshold scheme a secret quantum state is divided into n shares such that any k of those shares can be used to reconstruct the secret but any set of k ensuremath 1 or fewer shares contains absolutely no information about the secret we show that the only constraint on the existence of threshold schemes comes from the quantum no cloning theorem which requires that nl2k and we give efficient constructions of all threshold schemes we also show that for k ensuremath le nl2k ensuremath 1 then any k n threshold scheme must distribute information that is globally in a mixed state

analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation abstract the antiplane strain problem of two dissimilar anisotropic composite wedges of arbitrary angles that are bonded together along a common edge is considered the surfaces of the wedges can be subjected to traction traction traction displacement or displacement displacement boundary conditions the dependence of the order of the stress singularity on the wedge angles and material constants is studied the angular distribution of stresses at the apex and the exact full field stress solutions are also investigated explicit solutions for the order of stress singularity are obtained for some special cases it is found that the order of the stress singularity is always real for the antiplane dissimilar anisotropic wedge problem this is quite different from the in plane case in which the complex type of stress singularity might exist

existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time varying delays in this paper we study cellular neural networks with almost periodic variable coefficients and time varying delays by using the existence theorem of almost periodic solution for general functional differential equations introducing many real parameters and applying the lyapunov functional method and the technique of young inequality we obtain some sufficient conditions to ensure the existence uniqueness and global exponential stability of almost periodic solution the results obtained in this paper are new useful and extend and improve the existing ones in previous literature

security of epr based quantum cryptography against incoherent symmetric attacks we investigate a new strategy for incoherent eavesdropping in ekert s entanglement based quantum key distribution protocol we show that under certain assumptions of symmetry the effectiveness of this strategy reduces to that of the original single qubit protocol of bennett and brassard

selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function the concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks rnns with saturated piecewise linear transfer function a set of neurons is said to be selectable if it can be co unsaturated at a stable equilibrium point by some external input a set of neurons is said to be unselectable if it is not selectable i e such set of neurons can never be co unsaturated at any stable equilibrium point regardless of what the input is the importance of such concepts is that they enable a new perspective of the memory in rnns necessary and sufficient conditions for the existence of selectable and unselectable sets of neurons are obtained as an application the problem of group selection is discussed by using such concepts it shows that under some conditions each group is a selectable set and each selectable set is contained in some group thus groups are indicated by selectable sets of the rnns and can be selected by external inputs simulations are carried out to further illustrate the theory

some extensions of a new method to analyze complete stability of neural networks in a recent work a new method has been introduced to analyze complete stability of the standard symmetric cellular neural networks cnns which are characterized by local interconnections and neuron activations modeled by a three segment piecewise linear pwl function by complete stability it is meant that each trajectory of the neural network converges toward an equilibrium point the goal of this paper is to extend that method in order to address complete stability of the much wider class of symmetric neural networks with an additive interconnecting structure where the neuron activations are general pwl functions with an arbitrary number of straight segments the main result obtained is that complete stability holds for any choice of the parameters within the class of symmetric additive neural networks with pwl neuron activations i e such a class of neural networks enjoys the important property of absolute stability of global pattern formation it is worth pointing out that complete stability is proved for generic situations where the neural network has finitely many isolated equilibrium points as well as for degenerate situations where there are infinite nonisolated equilibrium points the extension in this paper is of practical importance since it includes neural networks useful to solve significant signal processing tasks e g neural networks with multilevel neuron activations it is of theoretical interest too due to the possibility of approximating any continuous function e g a sigmoidal function using pwl functions the results in this paper confirm the advantages of the method of forti and tesi with respect to lasalle approach to address complete stability of pwl neural networks

quantum games entropy abstract we propose the study of quantum games from the point of view of quantum information theory and statistical mechanics every game can be described by a density operator the von neumann entropy and the quantum replicator dynamics there exists a strong relationship between game theories information theories and statistical physics the density operator and entropy are the bonds between these theories the analysis we propose is based on the properties of entropy the amount of information that a player can obtain about his opponent and a maximum or minimum entropy criterion the natural trend of a physical system is to its maximum entropy state the minimum entropy state is a characteristic of a manipulated system i e externally controlled or imposed there exist tacit rules inside a system that do not need to be specified or clarified and search the system equilibrium based on the collective welfare principle the other rules are imposed over the system when one or many of its members violate this principle and maximize its individual welfare at the expense of the group

global asymptotic stability of delayed cellular neural networks a new criterion for the global asymptotic stability of the equilibrium point of cellular neural networks with multiple time delays is presented the obtained result possesses the structure of a linear matrix inequality and can be solved efficiently using the recently developed interior point algorithm a numerical example is used to show the effectiveness of the obtained result

quantum cryptography without bell s theorem ekert has described a cryptographic scheme in which einstein podolsky rosen epr pairs of particles are used to generate identical random numbers in remote places while bell s theorem certifies that the particles have not been measured in transit by an eavesdropper we describe a related but simpler epr scheme and without invoking bell s theorem prove it secure against more general attacks including substitution of a fake epr source finally we show our scheme is equivalent to the original 1984 key distribution scheme of bennett and brassard which uses single particles instead of epr pairs

multistability of neural networks with mexican hat type activation functions in this paper we are concerned with a class of neural networks with mexican hat type activation functions due to the different structure from neural networks with saturated activation functions a set of new sufficient conditions are presented to study the multistability including the total number of equilibrium points their locations and stability furthermore the attraction basins of stable equilibrium points are investigated for two neuron neural networks the investigation shows that the stable manifolds of unstable equilibrium points constitute the boundaries of attraction basins of stable equilibrium points several illustrative examples are given to verify the effectiveness of our results

entanglement of the antisymmetric state we analyse the entanglement of the antisymmetric state in dimension d d and present two main results first we show that the amount of secrecy that can be extracted from the state is low more precisely the distillable key is bounded by o 1 d second we show that the state is highly entangled in the sense that a large number of ebits are needed in order to create the state entanglement cost is larger than a constant independent of d the second result is shown to imply that the regularised relative entropy with respect to separable states is also lower bounded by a constant finally we note that the regularised relative entropy of entanglement is asymptotically continuous in the state elementary and advanced facts from the representation theory of the unitary group including the concept of plethysm play a central role in the proofs of the main results

analysis of perfectly bonded wedges and bonded wedges with an interfacial crack under antiplane shear loading antiplane shear deformation of perfectly bonded wedges as well as bonded wedges with an interface crack are studied in this paper the solution of governing differential equations is accomplished by means of the mellin transform for two edge bonded isotropic wedges with perfect bonding along the common edge closed form solutions are obtained for stress fields and analytical relations are given for the strength of singularity at the apex however for bonded wedges with an interfacial crack first it is necessary to express the traction free condition of the crack faces in the form of a singular integral equation which is done in this paper by describing an exact analytical method the resultant singular integral equations are then solved analytically and the obtained results including the stress intensity factors at the crack tips are plotted a comparison of the results in the special cases shows a complete agreement with those cited in the literature however when the crack tip coincides with the wedge apex a strength of singularity of unity has been observed

stability analysis of discrete time recurrent neural networks with stochastic delay this paper is concerned with the stability analysis of discrete time recurrent neural networks rnns with time delays as random variables drawn from some probability distribution by introducing the variation probability of the time delay a common delayed discrete time rnn system is transformed into one with stochastic parameters improved conditions for the mean square stability of these systems are obtained by employing new lyapunov functions and novel techniques are used to achieve delay dependence the merit of the proposed conditions lies in its reduced conservatism which is made possible by considering not only the range of the time delays but also the variation probability distribution a numerical example is provided to show the advantages of the proposed conditions

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

unconditionally secure cryptosystems based on quantum cryptography most modern cryptographic studies design cryptosystems and algorithms using mathematical concepts in designing and analyzing cryptosystems and protocols mathematical concepts are critical in supporting the claim that the intended cryptosystem is secure most early cryptographic algorithms are based either on factorization or on discrete logarithm problem such systems generally adopt rather simple mathematics and therefore need extensive secondary index computation this study discusses quantum cryptosystems protection of system security and optimization of system efficiency quantum cryptography detects intrusion and wiretap in quantum mechanics a wiretap is neither external nor passive rather it modifies its entity based on the internal component of the system the status of the quantum system changes once a wiretap is detected hence only the designer of the system can discover the quantum status of the system an eavesdropper can neither determine the quantum state nor duplicate the system the quantum cryptosystem can achieve unconditional security and thus guarantees secure communication

multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions this paper studies multiperiodicity and attractivity for a class of recurrent neural networks rnns with unsaturating piecewise linear transfer functions and variable delays using local inhibition conditions for boundedness and global attractivity are established these conditions allow coexistence of stable and unstable trajectories moreover multiperiodicity of the network is investigated by using local invariant sets it shows that under some interesting conditions there exists one periodic trajectory in each invariant set which exponentially attracts all trajectories in that region correspondingly simulations are carried out to illustrate the theories

quantum correlations and secret bits it is shown that i all entangled states can be mapped by single copy measurements into probability distributions containing secret correlations and ii if a probability distribution obtained from a quantum state contains secret correlations then this state has to be entangled these results prove the existence of a two way connection between secret and quantum correlations in the process of preparation they also imply that either it is possible to map any bound entangled state into a distillable probability distribution or bipartite bound information exists

entanglement transformation between sets of bipartite pure quantum states using local operations alice and bob are given an unknown initial state chosen from a set of pure quantum states their task is to transform the initial state to a corresponding final pure state using local operations only we prove necessary and sufficient conditions on the existence of such a transformation we also provide efficient algorithms that can quickly rule out the possibility of transforming a set of initial states to a set of final states

selectively grouping neurons in recurrent networks of lateral inhibition winner take all networks have been proposed to underlie many of the brain s fundamental computational abilities however not much is known about how to extend the grouping of potential winners in these networks beyond single neuron or uniformly arranged groups of neurons we show that competition between arbitrary groups of neurons can be realized by organizing lateral inhibition in linear threshold networks given a collection of potentially overlapping groups with the exception of some degenerate cases the lateral inhibition results in network dynamics such that any permitted set of neurons that can be coactivated by some input at a stable steady state is contained in one of the groups the information about the input is preserved in this operation the activity level of a neuron in a permitted set corresponds to its stimulus strength amplified by some constant sets of neurons that are not part of a group cannot be coactivated by any input at a stable steady state we analyze the storage capacity of such a network for random groups the number of random groups the network can store as permitted sets without creating too many spurious ones in this framework we calculate the optimal sparsity of the groups maximizing group entropy we find that for dense inputs the optimal sparsity is unphysiologically small however when the inputs and the groups are equally sparse we derive a more plausible optimal sparsity we believe our results are the first steps toward attractor theories in hybrid analog digital networks

independence of work and entropy for equal energetic finite quantum systems passive state energy as an entanglement quantifier although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic ee states in the asymptotic limit for the finite quantum systems the relation is not so linear and requires detailed investigation toward this we have considered a resource theoretic framework taking the energy preserving operations epos as free to compare the amount of extractable work from two different quantum states under the epo majorization becomes a necessary criterion for state transformation it is also shown that the passive state energy is a concave function and for ee states it becomes proportional to the ergotropy in absolute sense invariance of the passive state energy under unitary action on the given state makes it an entanglement measure for the pure bipartite states furthermore due to the nonadditivity of passive state energy for the different system hamiltonians one can generate vidal s monotones which would give the optimal probability for pure entangled state transformation this measure also quantifies the ergotropic gap which is employed to distinguish some specific classes of three qubit pure entangled states

non contextual chocolate balls versus value indefinite quantum cryptography some quantum cryptographic protocols can be implemented with specially prepared metaphorical chocolate balls representing local hidden variables others protected by value indefiniteness cannot this latter feature which follows from bell and kochen specker type arguments is only present in systems with three or more mutually exclusive outcomes conversely there exist local hidden variable models based on chocolate ball configurations utilizable for cryptography which cannot be realized by quantum systems the possibility that quantum cryptography supported by value indefiniteness contextuality has practical advantages over more conventional quantum cryptographic protocols remains highly speculative

singularities interacting with interfaces and cracks abstract solutions to singularities such as point force point moment edge dislocation and transformation strain spot embedded in bonded elastic blocks of dissimilar materials are found to relate to the solutions to the same singularities in an infinite homogeneous plane by a formula independent of the nature of the singularities this universal result is then used to analyze the interactions between singularities and interface cracks the complete solutions and stress intensity factors are presented for two important interface crack configurations