supersymmetric harry dym type equations a supersymmetric version is proposed for the well known harry dym system a general class super lax operator which leads to consistent equations is considered

the supersymmetric camassa holm equation and geodesic flow on the superconformal group we study a family of fermionic extensions of the camassa holm equation within this family we identify three interesting classes a equations which are inherently hamiltonian describing geodesic flow with respect to an h1 metric on the group of superconformal transformations in two dimensions b equations which are hamiltonian with respect to a different hamiltonian structure and c supersymmetric equations classes a and b have no intersection but the intersection of classes a and c gives a system with interesting integrability properties we demonstrate the painleve property for some simple but nontrivial reductions of this system and also discuss peakon type solutions

optimal indecomposable witnesses without extremality or the spanning property one of the interesting problems of optimal indecomposable entanglement witnesses is whether there exists an optimal indecomposable entanglement witness which neither has the spanning property nor is associated with an extremal positive linear map here we answer this question in the negative by examining the extremality of the positive linear maps constructed by qi and hou 2011 j phys a math theor 44 215305

positive finite rank elementary operators and characterizing entanglement of states in this paper some indecomposable positive finite rank elementary operators of order n n are constructed this allows us to give a simple necessary and sufficient criterion for the separability of pure states in bipartite systems of any dimension in terms of positive elementary operators of order 2 2 and obtain some new mixed entangled states that cannot be detected by the positive partial transpose criterion and the realignment criterion

complete positivity of the map from a basis to its dual basis the dual of a matrix ordered space has a natural matrix ordering that makes the dual space matrix ordered as well the purpose of these notes is to give a condition that describes when the linear map taking a basis of mn to its dual basis is a complete order isomorphism we exhibit natural orthonormal bases for mn such that this map is an order isomorphism but not a complete order isomorphism included among such bases is the pauli basis our results generalize the choi matrix by giving conditions under which the role of the standard basis eij can be replaced by other bases

optimal entanglement witnesses from generalized reduction and robertson maps we provide a generalization of the reduction and robertson positive maps in matrix algebras they give rise to a new class of optimal entanglement witnesses their structural physical approximation is analyzed as a byproduct we provide new examples of ppt positive partial transpose entangled states

optimal entanglement criterion for mixed quantum states we develop a strong and computationally simple entanglement criterion the criterion is based on an elementary positive map phi which operates on state spaces with even dimension n or 4 it is shown that phi detects many entangled states with a positive partial transposition ppt and that it leads to a class of optimal entanglement witnesses this implies that there are no other witnesses which can detect more entangled ppt states the map phi yields a systematic method for the explicit construction of high dimensional manifolds of bound entangled states

a new criterion for indecomposability of positive maps we give a criterion for a positive mapping on the space of operators on a hilbert space to be indecomposable we show that this criterion can be applied to two families of positive maps these families of maps can then be used to form separability criteria for bipartite quantum states that can detect the entanglement of bound entangled quantum states

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

generalized choi maps in three dimensional matrix algebra we consider a class of positive linear maps in the three dimensional matrix algebra which are generalizations of the positive linear map constructed by choi in the relation with positive semidefinite biquadratic forms we find conditions for which such maps are completely positive completely copositive decomposable and two positive

a super hierarchy of the vector nonlinear schrodinger equations and hamiltonian structures conservation laws a super hierarchy of the vector nonlinear schrodinger equations associated with the 3 3 matrix spectral problem is proposed by using the lenard recursion equations and the zero curvature equation the corresponding super bi hamiltonian structures are established with the help of the super trace identity furthermore we derive the infinite conservation flows of the super vector nonlinear schrodinger equation and the second equation in the hierarchy by utilizing spectral parameter expansions

cones of positive maps and their duality relations the structure of cones of positive and k positive maps acting on a finite dimensional hilbert space is investigated special emphasis is given to their duality relations to the sets of superpositive and k superpositive maps we characterize k positive and k superpositive maps with regard to their properties under taking compositions a number of results obtained for maps are also rephrased for the corresponding cones of block positive k block positive separable and k entangled operators due to the jamiolkowski choi isomorphism generalizations to a situation where no such simple isomorphism is available are also made employing the idea of mapping cones as a side result to our discussion we show that extreme entanglement witnesses which are optimal should be of special interest in entanglement studies

a series of absolutely indecomposable positive maps in matrix algebras abstract we provide examples of positive maps in m n c n 4 which cannot be decomposed into a sum of a 2 positive map and a 2 copositive map

the structural physical approximation conjecture it was conjectured that the structural physical approximation spa of an optimal entanglement witness is separable or equivalently that the spa of an optimal positive map is entanglement breaking this conjecture was disproved first for indecomposable maps and more recently for decomposable maps the arguments in both cases are sketched along with important related results this review includes background material on topics including entanglement witnesses optimality duality of cones decomposability and the statement and motivation for the spa conjecture so that it should be accessible for a broad audience

disproving the conjecture on the structural physical approximation to optimal decomposable entanglement witnesses we disprove the conjecture that structural physical approximations to optimal entanglement witnesses are separable states the conjecture holds true for extremal decomposable entanglement witnesses

the extended supersymmetrization of the multicomponent kadomtsev petviashvilli hierarchy we describe three different approaches to the extended n 2 supersymmetrization of the multicomponent kp hierarchy in the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as superfermions it is shown that many soliton equations can be embedded in the supersymmetry theory by using the first approach even if we do not change these equations in the bosonic limit of the supersymmetry in the second or third approach we obtain a generalization of the soliton equations in the bosonic limit which remains in the class of the usual commuting functions as a byproduct of our analysis we prove that for the first procedure the bosonic part of the one component supersymmetric kp hierarchy coincides with the usual classical two component kp hierarchy

choi matrices norms and entanglement associated with positive maps on matrix algebras abstract we study positive maps of b k into b h for finite dimensional hilbert spaces k and h our main emphasis is on how choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps special attention will be given to entanglement properties and k positive maps

rank two bipartite bound entangled states do not exist we explore the relation between the rank of a bipartite density matrix and the existence of bound entanglement we show a relation between the rank marginal ranks and distillability of a mixed state and use this to prove that any rank n bound entangled state must have support on no more than an n n hilbert space a direct consequence of this result is that there are no bipartite bound entangled states of rank two we also show that a separability condition in terms of a quantum entropy inequality is associated with the above results we explore the idea of how many pure states are needed in a mixture to cancel the distillable entanglement of a schmidt rank n pure state and provide a lower bound of n 1 we also prove that a mixture of a non zero amount of any pure entangled state with a pure product state is distillable

speed scaling to manage energy and temperature speed scaling is a power management technique that involves dynamically changing the speed of a processor we study policies for setting the speed of the processor for both of the goals of minimizing the energy used and the maximum temperature attained the theoretical study of speed scaling policies to manage energy was initiated in a seminal paper by yao et al 1995 and we adopt their setting we assume that the power required to run at speed s is p s e s for some constant 1 we assume a collection of tasks each with a release time a deadline and an arbitrary amount of work that must be done between the release time and the deadline yao et al 1995 gave an offline greedy algorithm yds to compute the minimum energy schedule they further proposed two online algorithms average rate avr and optimal available oa and showed that avr is 2 1 competitive with respect to energy we provide a tight bound on the competitive ratio of oa with respect to energy we initiate the study of speed scaling to manage temperature we assume that the environment has a fixed ambient temperature and that the device cools according to newton s law of cooling we observe that the maximum temperature can be approximated within a factor of two by the maximum energy used over any interval of length 1 b where b is the cooling parameter of the device we define a speed scaling policy to be cooling oblivious if it is simultaneously constant competitive with respect to temperature for all cooling parameters we then observe that cooling oblivious algorithms are also constant competitive with respect to energy maximum speed and maximum power we show that yds is a cooling oblivious algorithm in contrast we show that the online algorithms oa and avr are not cooling oblivious we then propose a new online algorithm that we call bkp we show that bkp is cooling oblivious we further show that bkp is e competitive with respect to the maximum speed and that no deterministic online algorithm can have a better competitive ratio bkp also has a lower competitive ratio for energy than oa for 5 finally we show that the optimal temperature schedule can be computed offline in polynomial time using the ellipsoid algorithm

separable states and the structural physical approximation of a positive map abstract we introduce a necessary condition for a state to be separable and apply this condition to the structural physical approximation of an optimal positive map and give a proof of the fact that the spa need not be separable

on hamiltonian perturbations of hyperbolic systems of conservation laws i quasi triviality of bi hamiltonian perturbations we study the general structure of formal perturbative solutions to the hamiltonian perturbations of spatially one dimensional systems of hyperbolic pdes vt v x 0 under certain genericity assumptions it is proved that any bi hamiltonian perturbation can be eliminated in all orders of the perturbative expansion by a change of coordinates on the infinite jet space depending rationally on the derivatives the main tool is in constructing the so called quasimiura transformation of jet coordinates eliminating an arbitrary deformation of a semisimple bi hamiltonian structure of hydrodynamic type the quasi triviality theorem we also describe following 35 the invariants ofsuchbi hamiltonian structures with respect to the group of miura type transformations depending polynomially on the derivatives c

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

on structural physical approximations and entanglement breaking maps very recently a conjecture saying that the so called structural physical approximations spas to optimal positive maps optimal entanglement witnesses give entanglement breaking eb maps separable states has been posed korbicz et al 2008 phys rev a 78 062105 the main purpose of this contribution is to explore this subject first we extend the set of entanglement witnesses supporting the conjecture then we ask whether spas constructed from other than the depolarizing channel maps also lead to eb maps and show that in general this is not the case on the other hand we prove an interesting fact that for any positive map there exists an eb channel such that the spa of constructed with the aid of is again an eb channel finally we ask similar questions in the case of continuous variable systems we provide a simple way of constructing spa and prove that in the case of the transposition map it gives the eb channel

supersymmetric extensions of the harry dym hierarchy we study the supersymmetric extensions of the harry dym hierarchy of equations we obtain the susy b extension the doubly susy b extension as well as the n 1 and the n 2 supersymmetric extensions for this system the n 2 supersymmetric extension is particularly interesting since it leads to new classical integrable systems in the bosonic limit we prove the integrability of these systems through the bi hamiltonian formulation of integrable models and through the lax description we also discuss the supersymmetric extension of the hunter zheng equation which belongs to the harry dym hierarchy of equations

an approach to generate superextensions of integrable systems an algorithm to generate integrable systems is extended to the super case some new examples of superextensions of integrable systems are illustrated we also generalize the trace identity due to tu to the super case and use it to establish hamiltonian structures of superextensions of integrable systems under consideration

the fully supersymmetric akns equations the general fully supersymmetric approach to the akns method is presented the supersymmetric kdv and mkdv equations are considered as examples the supersymmetric backlund transformation is constructed for the supersymmetric kdv equation

bihamiltonian geometry darboux coverings and linearization of the kp hierarchy we use ideas of the geometry of bihamiltonian manifolds developed by gel fand and zakharevich to study the kp equations in this approach they have the form of local conservation laws and can be traded for a system of ordinary differential equations of riccati type which we call the central system we show that the latter can be linearized by means of a darboux covering and we use this procedure as an alternative technique to construct rational solutions of the kp equations

exposed positive maps a sufficient condition exposed positive maps in matrix algebras define a dense subset of extremal maps we provide a sufficient condition for a positive map to be exposed this is an analogue of a spanning property which guarantees that a positive map is optimal we analyze a class of decomposable maps for which this condition is also necessary

entanglement witnesses arising from choi type positive linear maps we construct optimal pptes witnesses to detect 3 3 ppt entangled edge states of type 6 8 constructed recently by kye and osaka 2012 j math phys 53 052201 to do this we consider positive linear maps which are variants of the choi type map involving complex numbers and examine several notions related to the optimality of those entanglement witnesses throughout the discussion we suggest a method to check the optimality of entanglement witnesses without the spanning property

a class of exposed indecomposable positive maps exposed positive maps in matrix algebras define a dense subset of extremal maps we provide a class of indecomposable positive maps in the algebra of 2n 2n complex matrices with n 2 it is shown that these maps are exposed and hence define the strongest tool in entanglement theory to discriminate between separable and entangled states

supersymmetric extensions of the nonlinear schrodinger equation symmetries and coverings a construction is proposed for a supersymmetric generalization of the cubic schrodinger equation resulting in two supersymmetric systems one of which contains a free parameter both systems are proven to admit an infinite set of higher order local and nonlocal symmetries and a seemingly infinite set of conservation laws the lowest order terms of which are given explicitly moreover the theory of coverings equivalent to the prolongation method of wahlquist and estabrook is applied to both systems both are seen to admit an infinite dimensional covering algebra the structure of which is determined explicitly resulting in a related supersymmetric system of differential equations as well as an auto backlund transformation for each equation this indicates the complete integrability of both systems

an efficient algorithm for computing optimal discrete voltage schedules we consider the problem of job scheduling on a variable voltage processor with d discrete voltage speed levels we give an algorithm which constructs a minimum energy schedule for n jobs in o d n log n time previous approaches solve this problem by first computing the optimal continuous solution in o n 3 time and then adjusting the speed to discrete levels in our approach the optimal discrete solution is characterized and computed directly from the inputs we also show that o n log n time is required hence the algorithm is optimal for fixed d

indecomposable positive maps in low dimensional matrix algebras abstract we classify a series of positive maps in low dimensional matrix algebras with respect to the degree of indecomposability and provide stronger indecomposable maps in m n we also present a basic result about the atomic property

a note on the optimality of decomposable entanglement witnesses and completely entangled subspaces entanglement witnesses ews constitute one of the most important entanglement detectors in quantum systems nevertheless their complete characterization in particular with respect to the notion of optimality is still missing even in the decomposable case here we show that for any qubit qunit decomposable ew dew w the three statements are equivalent i the set of product vectors obeying e f w e f 0 spans the corresponding hilbert space ii w is optimal and iii w q with q denoting a positive operator supported on a completely entangled subspace ces and standing for the partial transposition while implications i ii and ii iii are known here we prove that iii implies i this is a consequence of a more general fact saying that product vectors orthogonal to any ces in span after partial conjugation the whole space on the other hand already in the case of the hilbert space there exist dews for which iii does not imply i consequently either i does not imply ii or ii does not imply iii and the above transparent characterization obeyed by qubit qunit dews does not hold in general

energy optimal schedules for jobs with multiple active intervals in this paper we study the scheduling problem of jobs with multiple active intervals each job in the problem instance has n n 1 disjoint active time intervals where it can be executed and a workload characterized by the required number of cpu cycles previously people studied multiple interval job scheduling problem where each job must be assigned enough cpu cycles in one of its active intervals we study a different practical version where the partial work done by the end of an interval remains valid and each job is considered finished if total cpu cycles assigned to it in all its active intervals reach the requirement the goal is to find a feasible schedule that minimizes energy consumption by adapting the algorithm for single interval jobs proposed in yao demers and shenker 1995 1 one can still obtain an optimal schedule however the two phases in that algorithm critical interval finding and scheduling the critical interval can no longer be carried out directly we present polynomial time algorithms to solve the two phases for jobs with multiple active intervals and therefore can still compute the optimal schedule in polynomial time

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result