Remarks on the combinatorial intersection cohomology of fans

We review the theory of combinatorial intersection cohomology of fans developed by Barthel-Brasselet-Fieseler-Kaup, Bressler-Lunts, and Karu. This theory gives a substitute for the intersection cohomology of toric varieties which has all the expected formal properties but makes sense even for non-rational fans, which do not define a toric variety. As a result, a number of interesting results on the toric $g$ and $h$ polynomials have been extended from rational polytopes to general polytopes. We present explicit complexes computing the combinatorial IH in degrees one and two; the degree two complex gives the rigidity complex previously used by Kalai to study $g_2$. We present several new results which follow from these methods, as well as previously unpublished proofs of Kalai that $g_k(P) = 0$ implies $g_k(P^*) = 0$ and $g_{k+1}(P) = 0$.Comment: 34 pages. Typos fixed; final version, to appear in Pure and Applied Math Quarterl

Large N lattice QCD and its extended strong-weak connection to the hypersphere

We calculate an effective Polyakov line action of QCD at large Nc and large Nf from a combined lattice strong coupling and hopping expansion working to second order in both, where the order is defined by the number of windings in the Polyakov line. We compare with the action, truncated at the same order, of continuum QCD on S^1 x S^d at weak coupling from one loop perturbation theory, and find that a large Nc correspondence of equations of motion found in \cite{Hollowood:2012nr} at leading order, can be extended to the next order. Throughout the paper, we review the background necessary for computing higher order corrections to the lattice effective action, in order to make higher order comparisons more straightforward.Comment: 33 pages, 7 figure

Components of Soft Computing for Epileptic Seizure Prediction and Detection

Components of soft computing include machine learning, fuzzy logic, evolutionary computation, and probabilistic theory. These components have the cognitive ability to learn effectively. They deal with imprecision and good tolerance of uncertainty. Components of soft computing are needed for developing automated expert systems. These systems reduce human interventions so as to complete a task essentially. Automated expert systems are developed in order to perform difficult jobs. The systems have been trained and tested using soft computing techniques. These systems are required in all kinds of fields and are especially very useful in medical diagnosis. This chapter describes the components of soft computing and review of some analyses regarding EEG signal classification. From those analyses, this chapter concludes that a number of features extracted are very important and relevant features for classifier can give better accuracy of classification. The classifier with a suitable learning method can perform well for automated epileptic seizure detection systems. Further, the decomposition of EEG signal at level 4 is sufficient for seizure detection

Full nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks

Dramatic progress has been made over the last decade in the numerical study of quantum chromodynamics (QCD) through the use of improved formulations of QCD on the lattice (improved actions), the development of new algorithms and the rapid increase in computing power available to lattice gauge theorists. In this article we describe simulations of full QCD using the improved staggered quark formalism, ``asqtad'' fermions. These simulations were carried out with two degenerate flavors of light quarks (up and down) and with one heavier flavor, the strange quark. Several light quark masses, down to about 3 times the physical light quark mass, and six lattice spacings have been used. These enable controlled continuum and chiral extrapolations of many low energy QCD observables. We review the improved staggered formalism, emphasizing both advantages and drawbacks. In particular, we review the procedure for removing unwanted staggered species in the continuum limit. We then describe the asqtad lattice ensembles created by the MILC Collaboration. All MILC lattice ensembles are publicly available, and they have been used extensively by a number of lattice gauge theory groups. We review physics results obtained with them, and discuss the impact of these results on phenomenology. Topics include the heavy quark potential, spectrum of light hadrons, quark masses, decay constant of light and heavy-light pseudoscalar mesons, semileptonic form factors, nucleon structure, scattering lengths and more. We conclude with a brief look at highly promising future prospects.Comment: 157 pages; prepared for Reviews of Modern Physics. v2: some rewriting throughout; references update

A model to address factors that could influence the information security behaviour of computing graduates

The fact that information is ubiquitous throughout most modern organisations cannot be denied. Information is not merely used as an enabler in modern organisations today, but is also used to gain a competitive advantage over competitors. Thus, information has become one of the most important business assets. It is, therefore, imperative that organisations protect information assets as they would protect other business assets. This is typically achieved through implementing various security measures.Technological and procedural security measures are largely dependent on humans. However, the incorrect behaviour of humans poses a significant threat to the protection of these information assets. Thus, it is vital to understand how human behaviour may impact the protection of information assets. While the focus of much literature is on organisations, the focus of this research is on higher education institutions and the factors of information security, with a specific focus on influencing the information security behaviour of computing graduates. Typically, computing graduates would be employed in organisations in various careers such as software developers, network administrators, database administrators and information systems analysts. Employment in these careers means that they would be closely interacting with information assets and information systems. A real problem, as identified by this research, is that currently, many higher education institutions are not consciously doing enough to positively influence the information security behaviour of their computing graduates. This research presents a model to address various factors that could influence the information security behaviour of computing graduates. The aim of this model is to assist computing educators in influencing computing graduates to adopt more secure behaviour, such as security assurance behaviour. A literature review was conducted to identify the research problem. A number of theories such as the Theory of Planned Behaviour, Protection Motivation Theory and Social Cognitive Theory were identified as being relevant for this research as they provided a theoretical foundation for factors that could influence the information security behaviour of computing graduates. Additionally, a survey was conducted to gather the opinions and perceptions of computing educators relating to information security education in higher education institutions. Results indicated that information security is not pervasively integrated within the higher education institutions surveyed. Furthermore, results revealed that most computing students were perceived to not be behaving in a secure manner with regard to information security. This could negatively influence their information security behaviour as computing graduates employed within organisations. Computing educators therefore require assistance in influencing the information security behaviour of these computing students. The proposed model to provide this assistance was developed through argumentation and modelling

The statistical-thermodynamic basis for computation of binding affinities: a critical review

Although the statistical thermodynamics of noncovalent binding has been considered in a number of theoretical papers, few methods of computing binding affinities are derived explicitly from this underlying theory. This has contributed to uncertainty and controversy in certain areas. This article therefore reviews and extends the connections of some important computational methods with the underlying statistical thermodynamics. A derivation of the standard free energy of binding forms the basis of this review. This derivation should be useful in formulating novel computational methods for predicting binding affinities. It also permits several important points to be established. For example, it is found that the double-annihilation method of computing binding energy does not yield the standard free energy of binding, but can be modified to yield this quantity. The derivation also makes it possible to define clearly the changes in translational, rotational, configurational, and solvent entropy upon binding. It is argued that molecular mass has a negligible effect upon the standard free energy of binding for biomolecular systems, and that the cratic entropy defined by Gurney is not a useful concept. In addition, the use of continuum models of the solvent in binding calculations is reviewed, and a formalism is presented for incorporating a limited number of solvent molecules explicitly

A model to address factors that could influence the information security behaviour of computing graduates

The fact that information is ubiquitous throughout most modern organisations cannot be denied. Information is not merely used as an enabler in modern organisations today, but is also used to gain a competitive advantage over competitors. Thus, information has become one of the most important business assets. It is, therefore, imperative that organisations protect information assets as they would protect other business assets. This is typically achieved through implementing various security measures.Technological and procedural security measures are largely dependent on humans. However, the incorrect behaviour of humans poses a significant threat to the protection of these information assets. Thus, it is vital to understand how human behaviour may impact the protection of information assets. While the focus of much literature is on organisations, the focus of this research is on higher education institutions and the factors of information security, with a specific focus on influencing the information security behaviour of computing graduates. Typically, computing graduates would be employed in organisations in various careers such as software developers, network administrators, database administrators and information systems analysts. Employment in these careers means that they would be closely interacting with information assets and information systems. A real problem, as identified by this research, is that currently, many higher education institutions are not consciously doing enough to positively influence the information security behaviour of their computing graduates. This research presents a model to address various factors that could influence the information security behaviour of computing graduates. The aim of this model is to assist computing educators in influencing computing graduates to adopt more secure behaviour, such as security assurance behaviour. A literature review was conducted to identify the research problem. A number of theories such as the Theory of Planned Behaviour, Protection Motivation Theory and Social Cognitive Theory were identified as being relevant for this research as they provided a theoretical foundation for factors that could influence the information security behaviour of computing graduates. Additionally, a survey was conducted to gather the opinions and perceptions of computing educators relating to information security education in higher education institutions. Results indicated that information security is not pervasively integrated within the higher education institutions surveyed. Furthermore, results revealed that most computing students were perceived to not be behaving in a secure manner with regard to information security. This could negatively influence their information security behaviour as computing graduates employed within organisations. Computing educators therefore require assistance in influencing the information security behaviour of these computing students. The proposed model to provide this assistance was developed through argumentation and modelling

Adiabatic perturbation theory and geometry of periodically-driven systems

We give a systematic review of the adiabatic theorem and the leading non-adiabatic corrections in periodically-driven (Floquet) systems. These corrections have a two-fold origin: (i) conventional ones originating from the gradually changing Floquet Hamiltonian and (ii) corrections originating from changing the micro-motion operator. These corrections conspire to give a Hall-type linear response for non-stroboscopic (time-averaged) observables allowing one to measure the Berry curvature and the Chern number related to the Floquet Hamiltonian, thus extending these concepts to periodically-driven many-body systems. The non-zero Floquet Chern number allows one to realize a Thouless energy pump, where one can adiabatically add energy to the system in discrete units of the driving frequency. We discuss the validity of Floquet Adiabatic Perturbation Theory (FAPT) using five different models covering linear and non-linear few and many-particle systems. We argue that in interacting systems, even in the stable high-frequency regimes, FAPT breaks down at ultra slow ramp rates due to avoided crossings of photon resonances, not captured by the inverse-frequency expansion, leading to a counter-intuitive stronger heating at slower ramp rates. Nevertheless, large windows in the ramp rate are shown to exist for which the physics of interacting driven systems is well captured by FAPT.The authors would like to thank M. Aidelsburger, M. Atala, E. Dalla Torre, N. Goldman, M. Heyl, D. Huse, G. Jotzu, C. Kennedy, M. Lohse, T. Mori, L. Pollet, M. Rudner, A. Russomanno, and C. Schweizer for fruitful discussions. This work was supported by AFOSR FA9550-16-1-0334, NSF DMR-1506340, ARO W911NF1410540, and the Hungarian research grant OTKA Nos. K101244, K105149. M. K. was supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors are pleased to acknowledge that the computational work reported in this paper was performed on the Shared Computing Cluster which is administered by Boston University's Research Computing Services. The authors also acknowledge the Research Computing Services group for providing consulting support which has contributed to the results reported within this paper. The study of the driven non-integrable transverse-field Ising model was carried out using QuSpin [185] - an open-source state-of-the-art Python package for dynamics and exact diagonalization of quantum many body systems, available to download here. (FA9550-16-1-0334 - AFOSR; DMR-1506340 - NSF; W911NF1410540 - ARO; K101244 - Hungarian research grant OTKA; K105149 - Hungarian research grant OTKA; DE-AC02-05CH11231 - Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab)https://arxiv.org/pdf/1606.02229.pd

The Dynamics of Vector-Borne Relapsing Diseases

We begin this dissertation with a review of the relevant history and theory behind disease modeling, investigating important motivating examples. The concept of the fundamental reproductive ratio of a disease, $R_0$, is introduced through these examples. The compartmental theory of disease spread and its results are introduced, particularly the next-generation method of computing $R_0$. We review center manifold theory, as it is critical to the reduction of the dimension of our problems. We review diseases that have a relapsing character and focus in on relapsing diseases that are spread by vectors in a host population. The primary example of such a disease is Tick-Borne Relapsing Fever (TBRF). Motivated by TBRF we establish a general model for the spread of a vector-borne relapsing disease. We then compare our model to current literature. With a model in hand we confirm that it meets the required hypotheses for the use of compartmental theory. A technical computation then leads to an explicit form of $R_0$ that is given in terms of the number of relapses. Further technical computations then allow us to describe the bifurcation at $R_0=1$, finding that it is always transcritical regardless of the number of relapses. We also show the existence of a unique endemic equilibrium for all values of $R_0$ greater than 1. Variations of the simple model are explored. Adding in removal to the recovered compartment, in which individuals leave an earlier relapse state and recover, we find how this changes $R_0$ and show that the bifurcation at $R_0$ is still transcritical. We investigate the addition of latent infective compartments and describe how they affect $R_0$. We also find the reproductive ratio when there are two host species that undergo the same number of relapses. We establish a continuity result between the reproductive ratios of systems with differing numbers of compartments. This allows us to state the reproductive ratio of a smaller system as a limit of the reproductive ratio of a larger system. This result is then used to compute the reproductive ratio for a coupled host-vector system where the hosts undergo a different number of relapses. We close with some conclusions and directions for future work