notes on a conservative nonlinear oscillator the amplitude frequency relationship is an important mathematical property for a nonlinear oscillator he s amplitude frequency formulation and the max min approach are used to handle the conservative nonlinear oscillator email protected email protected 2 x 0 for the amplitude frequency relationship the obtained result is compared with those in the open literature revealing the effectiveness of the used methods

random constraint satisfaction easy generation of hard satisfiable instances in this paper we show that the models of random csp instances proposed by xu and li k xu w li exact phase transitions in random constraint satisfaction problems journal of artificial intelligence research 12 2000 93 103 k xu w li many hard examples in exact phase transitions with application to generating hard satisfiable instances technical report corr report cs cc 0302001 revised version in theoretical computer science 355 2006 291 302 are of theoretical and practical interest indeed these models called rb and rd present several nice features first it is quite easy to generate random instances of any arity since no particular structure has to be integrated or property enforced in such instances then the existence of an asymptotic phase transition can be guaranteed while applying a limited restriction on domain size and on constraint tightness in that case a threshold point can be precisely located and all instances have the guarantee to be hard at the threshold i e to have an exponential tree resolution complexity next a formal analysis shows that it is possible to generate forced satisfiable instances whose hardness is similar to unforced satisfiable ones this analysis is supported by some representative results taken from an intensive experimentation that we have carried out using complete and incomplete search methods

probabilistic analysis of two heuristics for the 3 satisfiability problem an algorithm for the 3 satisfiability problem is presented and a probabilistic analysis is performed the analysis is based on an instance distribution which is parameterized to simulate a variety of sample characteristics the algorithm assigns values to variables appearing in a given instance of 3 satisfiability one at a time using the unit clause heuristic and a maximum occurring literal selection heuristic at each step a variable is chosen randomly from a subset of variables which is usually large the algorithm runs in polynomial time and it is shown that the algorithm finds a solution to a random instance of 3 satisfiability with probability bounded from below by a constant greater than zero for a range of parameter values the heuristics studied here can be used to select variables in a backtrack algorithm for 3 satisfiability experiments have shown that for about the same range of parameters as above the backtrack algorithm using the heuristics finds a solution in polynomial average time

a general model and thresholds for random constraint satisfaction problems in this paper we study the relation among the parameters in their most general setting that define a large class of random csp models d k csp where d is the domain size and k is the length of the constraint scopes the model d k csp unifies several related models such as the model rb and the model k csp we prove that the model d k csp exhibits exact phase transitions if klnd increases no slower than the logarithm of the number of variables a series of experimental studies with interesting observations are carried out to illustrate the solubility phase transition and the hardness of instances around phase transitions

zu geng s axiom vs cavalieri s theory when cavalieri found his theory in 1635 chinese mathematicians had used the theory for more than one millennium

threshold for monotone symmetric properties through a logarithmic sobolev inequality threshold phenomena are investigated using a general approach following talagrand ann probab 22 1994 1576 1587 and friedgut and kalai proc amer math soc 12 1999 1017 10541 the general upper bound for the threshold width of symmetric monotone properties is improved this follows from a new lower bound on the maximal influence of a variable on a boolean function the method of proof is based on a well known logarithmic sobolev inequality on 0 1 n this new bound is shown to be asymptotically optimal

revisiting the cavity method threshold for random 3 sat a detailed monte carlo study of the satisfiability threshold for random 3 sat has been undertaken in combination with a monotonicity assumption we find that the threshold for random 3 sat satisfie

strong noise sensitivity and random graphs the noise sensitivity of a boolean function describes its likelihood to flip under small perturbations of its input introduced in the seminal work of benjamini kalai and schramm 1999 it was there shown to be governed by the first level of fourier coefficients in the central case of monotone functions at a constant critical probability here we study noise sensitivity and a natural stronger version of it addressing the effect of noise given a specific witness in the original input our main context is the erdos renyi random graph where already the property of containing a given graph is sufficiently rich to separate these notions in particular our analysis implies strong noise sensitivity in settings where the bks criterion involving the first fourier level does not apply e g when the critical value goes to 0 polynomially fast in the number of variables

combinatorial sharpness criterion and phase transition classification for random csps we investigate the nature of the phase transition sharp or coarse for random constraint satisfaction problems we first give a sharp threshold criterion specified for csps which is derived from friedgut bourgain s one thus we get a complete and precise classification of the nature of the threshold for symmetric boolean csps in particular we show that it is governed by two local properties strongly related to the problems 1 sat and 2 xor sat

application of he s amplitude frequency formulation to a nonlinear oscillator with discontinuity in this paper he s amplitude frequency formulation is used to obtain a periodic solution of a nonlinear oscillator with discontinuity the accuracy arrives at 0 73 even when the amplitude tends to infinity

the max min approach to a relativistic equation this paper applies the max min approach proposed by ji huan he to the relativistic oscillator comparison with the exact solution shows that the method is very effective and convenient for solving nonlinear equations

on the phase transitions of random k constraint satisfaction problems constraint satisfaction has received increasing attention over the years intense research has focused on solving all kinds of constraint satisfaction problems csps in this paper first we propose a random csp model named k csp that guarantees the existence of phase transitions under certain circumstances the exact location of the phase transition is quantified and experimental results are provided to illustrate the performance of the proposed model second we revise the model k csp to a random linear csp by incorporating certain linear structure to constraint relations we also prove the existence of the phase transition and exhibit its exact location for this random linear csp model

approximate analysis of two mass spring systems and buckling of a column max min approach mma is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system after finding maximal and minimal solution thresholds of a nonlinear problem an approximate solution of the nonlinear equation can be easily achieved using he chengtian s interpolation numerical results indicate the effectiveness of the proposed method both in respect of the whole range of involved parameters as well as the excellent agreement with the approximate frequencies and periodic solutions with the exact ones it is predicted that mma can be found widely applicable in engineering

exact solution for nonlinear schrodinger equation by he s frequency formulation in this work we apply he s frequency formulation to search for the solution to nonlinear schrodinger equation three examples are given and the solutions obtained are in good accordance with wazwaz s solution abdul majid wazwaz a study on linear and nonlinear schrodinger equations by the variational iteration method chaos solitons fractals 37 4 2008 1136 1142 it is shown that he s frequency formulation is of utter straightforward and effective

a better algorithm for random k sat let boldsymbol phi be a uniformly distributed random k sat formula with n variables and m clauses we present a polynomial time algorithm that finds a satisfying assignment of boldsymbol phi with high probability for constraint densities m n 1 varepsilon k 2 k ln k k where varepsilon k rightarrow0 previously no efficient algorithm was known to find satisfying assignments with a nonvanishing probability beyond m n 1 817 cdot2 k k a frieze and s suen j algorithms 20 1996 pp 312 355

classifying the complexity of constraints using finite algebras many natural combinatorial problems can be expressed as constraint satisfaction problems this class of problems is known to be np complete in general but certain restrictions on the form of the constraints can ensure tractability here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra hence we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra we introduce a notion of tractable algebra and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it including its subalgebras and homomorphic images this allows us to reduce significantly the types of algebras which need to be classified using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently then so can the corresponding search problem we then classify all finite strictly simple surjective algebras with respect to tractability obtaining a dichotomy theorem which generalizes schaefer s dichotomy for the generalized satisfiability problem finally we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem

on the critical percolation probabilities we prove that the critical probabilities of site percolation on the square lattice satisfy the relation p c p 1 furthermore we prove the continuity of the function percolation probability

application of he chengtian s interpolation to bethe equation in this work he chengtian s interpolation which has millennial history is applied to the bethe equation the result shows that the present technology is very convenient and effective

surrogate analysis for detecting nonlinear dynamics in normal vowels normal vowels are known to have irregularities in the pitch to pitch variation which is quite important for speech signals to be perceived as natural human sound such pitch to pitch variation of vowels is studied in the light of nonlinear dynamics for the analysis five normal vowels recorded from three male and two female subjects are exploited where the vowel signals are shown to have normal levels of the pitch to pitch variation first by the false nearest neighbor analysis nonlinear dynamics of the vowels are shown to be well analyzed by using a relatively low dimensional reconstructing dimension of 4 d 7 then we further studied nonlinear dynamics of the vowels by spike and wave surrogate analysis the results imply that there exists nonlinear dynamical correlation between one pitch waveform pattern to another in the vowel signals on the basis of the analysis results applicability of the nonlinear prediction technique to vowel synthesis is discussed

pressure flow relationships in two models of the larynx having rectangular glottal shapes the pressure flow equations used in computer simulation studies of phonation lack experimental validation two polyester resin models of the laryngeal airway with rectangular glottal ducts were constructed in order to obtain the relationships between translaryngeal pressure drop and volume flow through the airway the results are in disagreement with the early estimates of wegel bell syst tech j 9 207 227 1930 but match the predictions given by ishizaka and matsudaira scrl monograph no 8 1972 to within approximately 10 for typical translaryngeal pressures for speech with larger discrepancies being found for the model with the larger glottal diameter the equation given by van den berg et al j acoust soc am 29 626 631 1957 may not be properly compared because their supraglottal pressure hole location may have been different from that used in the present study the data from the two models also are compared to recent empirical studies using an enlarged model of the larynx j gauffin et al conference on vocal fold physiology madison 1981

satisfiability allows no nontrivial sparsification unless the polynomial time hierarchy collapses consider the following two player communication process to decide a language l the first player holds the entire input x but is polynomially bounded the second player is computationally unbounded but does not know any part of x their goal is to decide cooperatively whether x belongs to l at small cost where the cost measure is the number of bits of communication from the first player to the second player for any integer d 3 and positive real e we show that if satisfiability for n variable d cnf formulas has a protocol of cost o nd e then conp is in np poly which implies that the polynomial time hierarchy collapses to its third level the result even holds when the first player is conondeterministic and is tight as there exists a trivial protocol for e 0 under the hypothesis that conp is not in np poly our result implies tight lower bounds for parameters of interest in several areas namely sparsification kernelization in parameterized complexity lossy compression and probabilistically checkable proofs by reduction similar results hold for other np complete problems for the vertex cover problem on n vertex d uniform hypergraphs this statement holds for any integer d 2 the case d 2 implies that no np hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of o k2 e edges unless conp is in np poly where k denotes the size of the deletion set kernels consisting of o k2 edges are known for several problems in the class including vertex cover feedback vertex set and bounded degree deletion

periodic solutions for some strongly nonlinear oscillations by he s variational iteration method in this paper we implement a new analytical technique he s variational iteration method for some strongly nonlinear oscillations a correction functional is constructed by using a general lagrange multiplier which can be identified via the variational theory the obtained approximate solutions and periods are compared with exact or numerical results to verify the effectiveness and accuracy of the method

locating the phase transition in binary constraint satisfaction problems abstract the phase transition in binary constraint satisfaction problems i e the transition from a region in which almost all problems have many solutions to a region in which almost all problems have no solutions as the constraints become tighter is investigated by examining the behaviour of samples of randomly generated problems in contrast to theoretical work which is concerned with the asymptotic behaviour of problems as the number of variables becomes larger this paper is concerned with the location of the phase transition in finite problems the accuracy of a prediction based on the expected number of solutions is discussed it is shown that the variance of the number of solutions can be used to set bounds on the phase transition and to indicate the accuracy of the prediction a class of sparse problems for which the prediction is known to be inaccurate is considered in detail it is shown that for these problems the phase transition depends on the topology of the constraint graph as well as on the tightness of the constraints

rebuild of king fang 40 bc musical scales by he s inequality he chengtian s inequality is used to re build the king fang s musical scales 41 24 and 53 31 in 40 bc the technology which might be little known to the west has been used for millennia by ancient chinese and can be powerfully applied to nonlinear problems

some interpolation formulas in chinese ancient mathematics when newton found his interpolation formula in 1670 ancient chinese mathematicians had used the formula in more sophisticated forms for more than one millennium a new proof to those formulas are geometrically illustrated

an in vitro setup to test the relevance and the accuracy of low order vocal folds models an experimental setup and human vocal folds replica able to produce self sustained oscillations are presented the aim of the setup is to assess the relevance and the accuracy of theoretical vocal folds models the applied reduced mechanical models are a variation of the classical two mass model and a simplification inspired on the delayed mass model for which the coupling between the masses is expressed as a fixed time delay the airflow is described as a laminar flow with flow separation the influence of a downstream resonator is taken into account the oscillation pressure threshold and fundamental frequency are predicted by applying a stability analysis to the mechanical models the measured frequency response of the mechanical replica together with the initial rest area allows us to determine the model parameters spring stiffness damping geometry masses validation of theoretical model predictions to experimental data shows the relevance of low order models in gaining a qualitative understanding of phonation however quantitative discrepancies remain large due to an inaccurate estimation of the model parameters and the crudeness in either flow or mechanical model description as an illustration it is shown that significant improvements can be made by accounting for viscous flow effects

an ancient chinese mathematical algorithm and its application to nonlinear oscillators an ancient chinese mathematical method is briefly introduced and its application to nonlinear oscillators is elucidated where he s amplitude frequency formulation is outlined three examples are given to show the extremely simple solution procedure and remarkably accurate solutions

generalized satisfiability problems minimal elements and phase transitions we develop a probabilistic model on the generalized satisfiability problems defined by schaefer in proceedings of the 10th stoc san diego ca usa association for computing machinery new york 1978 pp 216 226 for which the arity of the constraints is fixed in order to study the associated phase transition we establish new results on minimal elements associated with such generalized satisfiability problems these results are the keys of the exploration we conduct on the location and on the nature of the phase transition for generalized satisfiability we first prove that the phase transition occurs at the same scale for every reasonable problem and we provide lower and upper bounds for the associated critical ratio our framework allows one to get these bounds in a uniform way in particular we obtain a lower bound proportional to the number of variables for k sat without analyzing any algorithm finally we reveal the seed of coarseness for the phase transition of generalized satisfiability 2 xor sat

approximate solutions for nonlinear oscillation of a mass attached to a stretched elastic wire in this paper the approximate solutions of the mathematical model of a mass attached to a stretched elastic wire are presented at the beginning of the study the equation of motion is derived in a detailed way he s max min approach he s frequency amplitude method and the parameter expansion method are implemented to solve the established model the numerical results are further compared with the approximate analytical solutions for both a small and large amplitude of oscillations and a very good agreement is observed the relative errors are computed to illustrate the strength of agreement between the numerical and approximate analytical results

constructing an asymptotic phase transition in random binary constraint satisfaction problems the standard models used to generate random binary constraint satisfaction problems are described at the problem sizes studied experimentally a phase transition is seen as the constraint tightness is varied however achlioptas et al showed that if the problem size number of variables increases while the remaining parameters are kept constant asymptotically almost all instances are unsatisfiable in this paper an alternative scheme for one of the standard models is proposed in which both the number of values in each variable s domain and the average degree of the constraint graph are increased with problem size it is shown that with this scheme there is asymptotically a range of values of the constraint tightness in which instances are trivially satis able with probability at least 0 5 and a range in which instances are almost all unsatisfiable hence there is a crossover point at some value of the constraint tightness between these two ranges this scheme is compared to a similar scheme due to xu and li

solution of nonlinear equations by an ancient chinese algorithm in this paper we re study an ancient chinese algorithm the ying buzu shu in about second century bc known as the rule of double false position in west after 1202 ad the method can powerfully applied to solve nonlinear equations some examples are given

an empirical study of phase transitions in binary constraint satisfaction problems abstract an empirical study of randomly generated binary constraint satisfaction problems reveals that for problems with a given number of variables domain size and connectivity there is a critical level of constraint tightness at which a phase transition occurs at the phase transition problems change from being soluble to insoluble and the difficulty of problems increases dramatically a theory developed by williams and hogg 44 and independently developed by smith 37 predicts where the hardest problems should occur it is shown that the theory is in close agreement with the empirical results except when constraint graphs are sparse

upper bounds on the satisfiability threshold we present a survey of upper bounds which has been established up to now on the satisfiability threshold of random k sat formulae the ideas which led to these bounds and the techniques used to obtain them are explained a companion paper in this volume present a survey of the lower bounds

bicolouring random hypergraphs we study the problem of bicolouring random hypergraphs both numerically and analytically we apply the zero temperature cavity method to find analytical results for the phase transitions dynamic and static in the one step replica symmetry breaking 1rsb approximation these points appear to be in agreement with the results of the numerical algorithm in the second part we implement and test the survey propagation algorithm for specific bicolouring instances in the so called hard sat phase

thresholds of random quasi abelian codes for a q ary random quasi abelian code with fixed coindex and constant rate r it is shown that the gilbert varshamov gv bound is a threshold point if r is less than the gv bound at 0 1 q 1 then the probability of the relative distance of the random code being greater than approaches 1 as the index goes to infinity whereas if r is bigger than the gv bound at then the probability approaches 0 as a corollary there exist numerous asymptotically good quasi abelian codes attaining the gv bound

analysis of a nonlinear oscillator with discontinuity in this paper a nonlinear oscillator with discontinuity is analyzed using he s amplitude frequency formulation the natural frequency of the oscillator system can be obtained using concise and straightforward calculation steps good agreement between the results from the proposed and other classical approaches is reached

low dimensional models of the glottal flow incorporating viscous inviscid interaction the behavior of glottal flow can to a large extent be characterized by development and separation of the boundary layer the point of flow separation is known to vary during the phonatory cycle due to change in channel configuration to take the movable nature of the separation point into account the boundary layer equation is solved numerically and the values of the characteristic quantities are determined as well as the point of separation development of the boundary layer in general reduces the effective size of the channel and therefore increases the core flow velocity which in turn provides the boundary condition of the boundary layer equation the interaction between the viscous boundary layer and inviscid core flow parts of the glottal flow is therefore strongly indicated to apply this viscous inviscid interaction the expression of the core flow is derived for a two dimensional flow field and is solved jointly with the boundary layer equation numerical results are shown to examine the effect of the reynolds number and glottal configuration with special emphasis on the comparison of flow models developed for one and two dimensional flow fields numerical results are also quantitatively compared with data obtained from flow measurement experiments

a quantum lovasz local lemma the lovasz local lemma lll is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of weakly dependent criteria we show that the lll extends to a much more general geometric setting where events are replaced with subspaces and probability is replaced with relative dimension which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions our result immediately applies to the k qsat problem quantum analog of k sat for instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most 2k e k of them has a joint satisfiable state we then apply our results to the recently studied model of random k qsat recent works have shown that the satisfiable region extends up to a density of 1 in the large k limit where the density is the ratio of projectors to qubits using a hybrid approach building on work by laumann et al 2009 2010 we greatly extend the known satisfiable region for random k qsat to a density of 2k k2 since our tool allows us to show the existence of joint satisfying states without the need to construct them we are able to penetrate into regions where the satisfying states are conjectured to be entangled avoiding the need to construct them which has limited previous approaches to product states

intraglottal pressure profiles for a symmetric and oblique glottis with a divergence angle of 10 degrees human phonation does not always involve symmetric motions of the two vocal folds asymmetric motions can create slanted or oblique glottal angles this study reports intraglottal pressure profiles for a plexiglas model of the larynx with a glottis having a 10 degree divergence angle and either a symmetric orientation or an oblique angle of 15 degrees for the oblique glottis one side was divergent and the other convergent the vocal fold surfaces had 14 pressure taps the minimal glottal diameter was held constant at 0 04 cm results indicated that for either the symmetric or oblique case the pressure profiles were different on the two sides of the glottis except for the symmetric geometry for a transglottal pressure of 3 cm h2o for the symmetric case flow separation created lower pressures on the side where the flow stayed attached to the wall and the largest pressure differences between the two sides of the channel were 5 6 of the transglottal pressure for the oblique case pressures were lower

he s frequency amplitude formulation for the duffing harmonic oscillator he s frequency amplitude formulation is used to solve the duffing harmonic oscillator problem the solution procedure is simple and the result obtained is valid for the whole solution domain with high accuracy

sharp thresholds of graph properties and the sat problem consider g n p to be the probability space of random graphs on n vertices with edge probability p we will be considering subsets of this space defined by monotone graph properties a monotone graph property p is a property of graphs such that a p is invariant under graph automorphisims b if graph h has property p then so does any graph g having h as a subgraph a monotone symmetric family of graphs is a family defined by such a property one of the first observations made about random graphs by erdos and renyi in their seminal work on random graph theory 12 was the existence of threshold phenomena the fact that for many interesting properties p the probability of p appearing in g n p exhibits a sharp increase at a certain critical value of the parameter p bollobas and thomason proved the existence of threshold functions for all monotone set properties 6 and in 14 it is shown that this behavior is quite general and that all monotone graph properties exhibit threshold behavior i e the probability of their appearance increases from values very close to 0 to values close to 1 in a very small interval more precise analysis of the size of the threshold interval is done in 7 this threshold behavior which occurs in various settings which arise in combinatorics and computer science is an instance of the phenomenon of phase transitions which is the subject of much interest in statistical physics one of the main questions that arises in studying phase transitions is how sharp is the transition for example one of the motivations for this paper arose from the question of the sharpness of the phase transition for the property of satisfiability of a random kcnf boolean formula nati linial who introduced me to this problem suggested that although much concrete analysis was being performed on this problem the best approach would be to find general conditions for sharpness of the phase transition answering the question posed in 14 as to the relation between the length of the threshold interval and the value of the critical probability in this paper we indeed introduce a simple condition and prove it is sufficient stated roughly in the setting of random graphs the main theorem states that if a property has a coarse threshold then it can be approximated by the property of having certain given graphs as a subgraph this condition can be applied in a more

he s frequency amplitude formulation for nonlinear oscillators with an irrational force in this paper he s frequency amplitude formulation is applied to determine the periodic solution for a nonlinear oscillator system with an irrational force comparison with the exact solution shows that the result obtained is of high accuracy

lower bounds for random 3 sat via differential equations it is widely believed that the probability of satisfiability for random k sat formulae exhibits a sharp threshold as a function of their clauses to variables ratio for the most studied case k 3 there have been a number of results during the last decade providing upper and lower bounds for the threshold s potential location all lower bounds in this vein have been algorithmic i e in each case a particular algorithm was shown to satisfy random instances of 3 sat with probability 1 o 1 if the clauses to variables ratio is below a certain value we show how differential equations can serve as a generic tool for analyzing such algorithms by rederiving most of the known lower bounds for random 3 sat in a simple uniform manner

influence of collision on the flow through in vitro rigid models of the vocal folds measurements of pressure in oscillating rigid replicas of vocal folds are presented the pressure upstream of the replica is used as input to various theoretical approximations to predict the pressure within the glottis as the vocal folds collide the classical quasisteady boundary layer theory fails it appears however that for physiologically reasonable shapes of the replicas viscous effects are more important than the influence of the flow unsteadiness due to the wall movement a simple model based on a quasisteady bernoulli equation corrected for viscous effect combined with a simple boundary layer separation model does globally predict the observed pressure behavior

viscous effects in a static physical model of the uniform glottis the classic work on laryngeal flow resistance by van den berg et al j acoust soc am 29 626 631 1957 is revisited these authors used a formula to summarize their measurements and thus they separated the effects of entrance loss and pressure recovery from those of viscosity within the glottis analysis of intraglottal pressure distributions obtained from the physical model m5 r scherer et al j acoust soc am 109 1616 1630 2001 reveals substantial regions within the glottis where the pressure gradient is almost constant for glottal diameters from 0 005 to 0 16 cm as expected when viscous effects dominate the flow resistance of a narrow channel for this set of glottal diameters the part of the pressure gradient that has a linear dependence on the glottal volume velocity is isolated the inverse cube diameter of the poiseuille expression for glottal flows is examined with the data set provided by the m5 intraglottal pressure distributions the poiseuille effect is found to give a reasonable account of viscous effects in the diameter interval from 0 0075 to 0 02 cm but an inverse 2 59 power law gives a closer fit across all diameters

clustering phase of a general constraint satisfaction problem model d k csp abstract relation between problem hardness and solution space structure is an important research aspect model d k csp is a random model of constraint satisfaction problem which generates very hard instances when r 1 or r is near 1 where r represents normalized constraint density we study the clustering phase of the model and find that if r is below and close to 1 the solution space contains many widely distributed and well separated small frozen clusters which should be the reason why the generated instances are hard to solve

he chengtian s inequality and its applications he chengtian 369 447 ad is a famous ancient chinese mathematician and astronomer he proposes an iteration technique for searching for high accurate approximate values for one moon 29399752 days and one year 365150608 days respectively this paper re studies the he chengtian s inequality which might be new to the west

on russo s approximate zero one law consider the product measure mu p on 0 1 n when 0 operatorname resp 1 is given weight 1 p operatorname resp p consider a monotone subset a of 0 1 n we give a precise quantitative form to the following statement if a does not depend much on any given coordinate d mu p a dp is large thus in that case there is a threshold effect and mu p a jumps from near 0 to near 1 in a small interval

bootstrap percolation on the hypercube in the bootstrap percolation on the n dimensional hypercube in the initial position each of the 2n sites is occupied with probability p and empty with probability 1 p independently of the state of the other sites every occupied site remains occupied for ever while an empty site becomes occupied if at least two of its neighbours are occupied if at the end of the process every site is occupied we say that the initial position spans the hypercube we shall show that there are constants c1 c2 0 such that for open image in new window the probability of spanning tends to 1 as n while for open image in new window the probability tends to 0 furthermore we shall show that for each n the transition has a sharp threshold function

ant colony algorithm with a strengthened negative feedback mechanism for constraint satisfaction problems describing the definition and usage of negative feedback in ant colony optimization proposing a new negative pheromone matrix and combined with positive pheromone matrix in probability formula a novel strengthening negative feedback mechanism is proposed to improve efficiency and avoid local optimal detail experiment design has been given for evaluating the proposed approaches based on different standard real datasets and synthetically generated datasets ant colony optimization aco is an efficient way to solve binary constraint satisfaction problems csps in recent years new improvements have only considered enhancing the positive feedback to increase the convergence speed however through the study and analysis of these enhanced aco algorithms we determined that they still suffer from the problem of easily getting in locally optimal solutions thus an improved aco algorithm with a strengthened negative feedback mechanism is designed to tackle csps this new algorithm takes advantage of search history information and continually obtains failure experience to guide the ant swarm exploring the unknown space during the optimization process the starting point of this algorithm is to utilize the negative feedback to improve the diversity of solutions finally we use 24 csp samples and 25 queen samples to perform experiments compare this algorithm with other related algorithms and conduct performance assessment the preliminary results show that aco with negative feedback outperforms the compared algorithms in identifying high quality solutions

the scaling window of the model d k csp abstract consider the model d k csp which consists of a set of n variables with the domain size d and a set of t r n ln d ln p constraints where each constraint binds k distinct variables and permits p d k tuples of values we prove that the exact phase transition of the model d k csp occurs at r c 1 as long as k ln d ln n where satisfies that 1 2 1 2 2 k 1 e 1 e 0 is a sufficiently small constant more importantly we establish the finite size scaling about this transition specifically let 0 be a given constant the probability of satisfiability of the model d k csp is greater than 1 if r 1 1 n 1 ln d is dependent on the control parameters and is less than if r 1 1 n ln d

many hard examples in exact phase transitions this paper analyzes the resolution complexity of two random constraint satisfaction problem csp models i e model rb rd for which we can establish the existence of phase transitions and identify the threshold points exactly by encoding csps into cnf formulas it is proved that almost all instances of model rb rd have no tree like resolution proofs of less than exponential size thus we not only introduce new families of csps and cnf formulas hard to solve which can be useful in the experimental evaluation of csp and sat algorithms but also propose models with both many hard instances and exact phase transitions finally conclusions are presented as well as a detailed comparison of model rb rd with the hamiltonian cycle problem and random 3 sat which respectively exhibit three different kinds of phase transition behavior in np complete problems