Search

We introduce a numerical invariant \beta(K) of a knot K which measures how non-alternating K is. We prove an inequality between \beta (K) and the (knot Floer) thickness of K. As an application we show that all Montesinos knots have thickness at most one., Comment: 7 pages, 5 figures

Let and be fixed integer numbers. Assume that (a2+b2+c) is divisible by (ab+d) for some natural numbers a and b. Then the value of the fraction $$k ( = {(a^2+b^2+c) \over (ab+d)})$$ remains the same. Statement of this kind will be proved in pp. 1-3 and illustrated on some examples in pp. 3-10. The general method of proofs will be unified and simplified. Computing support will be provided: in pages 11-19 a simple program code is defined with the help of which one can hunt for natural numbers a, b with the same integer values of c, d and k. Here, a number of examples are given as well.

Knot Floer homology is a knot invariant defined using holomorphic curves. In more recent work, taking cues from bordered Floer homology,the authors described another knot invariant, called "bordered knot Floer homology", which has an explicit algebraic and combinatorial construction. In the present paper, we extend the holomorphic theory to bordered Heegaard diagrams for partial knot projections, and establish a pairing result for gluing such diagrams, in the spirit of the pairing theorem of bordered Floer homology. After making some model calculations, we obtain an identification of a variant of knot Floer homology with its algebraically defined relative. These results give a fast algorithm for computing knot Floer homology., Comment: 165 pages

The greatest loss of biodiversity in the EU has occurred on agricultural land. The Common Starling (Sturnus vulgaris) is one of the many numerous and widespread European farmland breeding bird species showing major population declines linked to European agricultural intensification. Here we present results based on monitoring data collected since 1975 in 24 countries to examine the influence of changing extent of grassland and cattle abundance (based on results of earlier studies showing the importance of lowland cattle grazed grassland for the species), wintering provenance and temperature on nationalbreeding population trends of Starlings across Europe. Positive Starling population trends in Central-East Europe contrast with negative trends in North and West Europe. Based on this indicative approach, we found some support for the importance of cattle stock and no support for grassland, temperature or wintering provenance to explain Starling population trends in Europe. However, we acknowledge such a European-wide analysis may conceal regional differences in responses and suggest that currently accessible national land use data might be insufficient to describe the detailed current changes in animalhusbandry and grassland management that may be responsible for changes in food availability and hence breeding Starling abundance and their differences across Europe. Reviewing results from local studies relating Starling population trends to local agricultural change offer contradictory results, suggesting complex interacting processes at work. We recommend combining national datasets on demography, land-use/agricultural practices and from autecological research to better explain the reasons for contrasting Starling trends across Europe, to enable us to predict how changing agriculture will affect Starlings and potentially suggest mitigation measures to restore local populations wherepossible.

Over one hundred editions (excluding reprints) have been prepared of the Solo Cello Suites of J. S. Bach, and the reasons for this extraordinary number have never been properly investigated; nor have these editions ever been collated, catalogued and analysed. Due to the lack of a surviving autograph we have to rely on four highly problematic manuscript sources which have over time been interpreted in a myriad of ways. This may be in part the explanation for the multiplicity of editions spanning almost two centuries. The first half of this thesis reviews the source history of the Suites. Not many cellists or scholars would argue with the view that Anna Magdalena Bach’s copy is considered to be the most trustworthy of these manuscript copies, despite its numerous copying errors. This study, however, provides evidence proposing that the very first copy of the Suites, made by Johann Peter Kellner, might have been based on a revised autograph, which could be of a higher quality than the model of any of the other copies. This evidence suggests that a significant number of previously accepted primary parameters (pitches and rhythms) in the Suites have to be revisited, and the alternatives transmitted through Kellner’s copy newly considered. Changes to the musical text in various editions are often due to changing editorial methodologies. The diverse approaches can be best observed through a transparent categorisation system, which can place any edition into its appropriate place within the temporal and editorial spectrum. One of the most important categories, that of the critical editions, seems to be defined historically in loose and somewhat contradictory terms; in order to assist this investigation, a robust definition for a critical edition is provided. The wide range of alternative readings in all areas of the musical text is apparent in most categories. To demonstrate this, the second half of the thesis analyses a number of detailed examples from the various categories. The surveyed examples suggest that repeating the efforts of the past with minor differences will not produce a single ‘ideal’ edition. In the concluding chapter I propose a completely different editorial approach: a digital edition, collating the existing sources and selected editions, in which the discrepancies are transparently overlaid, and easily identified, could offer an educated choice to future readers.

Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the distinguishability of the distributions, by optimizing a lower bound on test power for a statistical test using these features. The result is a parsimonious and interpretable indication of how and where two distributions differ locally. An empirical estimate of the test power criterion converges with increasing sample size, ensuring the quality of the returned features. In real-world benchmarks on high-dimensional text and image data, linear-time tests using the proposed semimetrics achieve comparable performance to the state-of-the-art quadratic-time maximum mean discrepancy test, while returning human-interpretable features that explain the test results.

Kernel methods represent one of the most powerful tools in machine learning to tackle problems expressed in terms of function values and derivatives due to their capability to represent and model complex relations. While these methods show good versatility, they are computationally intensive and have poor scalability to large data as they require operations on Gram matrices. In order to mitigate this serious computational limitation, recently randomized constructions have been proposed in the literature, which allow the application of fast linear algorithms. Random Fourier features (RFF) are among the most popular and widely applied constructions: they provide an easily computable, low-dimensional feature representation for shift-invariant kernels. Despite the popularity of RFFs, very little is understood theoretically about their approximation quality. In this paper, we provide a detailed finite-sample theoretical analysis about the approximation quality of RFFs by (i) establishing optimal (in terms of the RFF dimension, and growing set size) performance guarantees in uniform norm, and (ii) presenting guarantees in $L^r$ ($1\le r, Comment: To appear at NIPS-2015

The goal of this paper is to extend independent subspace analysis (ISA) to the case of (i) nonparametric, not strictly stationary source dynamics and (ii) unknown source component dimensions. We make use of functional autoregressive (fAR) processes to model the temporal evolution of the hidden sources. An extension of the ISA separation principle--which states that the ISA problem can be solved by traditional independent component analysis (ICA) and clustering of the ICA elements--is derived for the solution of the defined fAR independent process analysis task (fAR-IPA): applying fAR identification we reduce the problem to ISA. A local averaging approach, the Nadaraya-Watson kernel regression technique is adapted to obtain strongly consistent fAR estimation. We extend the Amari-index to different dimensional components and illustrate the efficiency of the fAR-IPA approach by numerical examples., Comment: 9 pages, 3 figures

The main goal in this paper is to point out that quantity $||\nabla R||^2(p)$ on a harmonic space can not be determined by the spectra of local geodesic spheres or balls, therefore the main results of [AM-S] (quoted in the title) are wrong. My strong interest in the above theorem is motivated by the fact that it contradicts some of my isospectrality examples constructed on geodesic spheres and balls of certain harmonic manifolds. The authors overlooked that the Lichnerowicz identity is not determined by the given spectral data, and so is the final crucial equation obtained by eliminating with the Lichnerowicz identity. In short, the above theorem has falsely been established by spectrally undetermined identities which can not be computed (determined) by the spectra of local geodesic spheres. More complicated spectrally undetermined functions cause the problems also in case of local geodesic balls. I describe also a strong physical argument which clearly explains why the manifolds appearing in my examples are isospectral. It must be pointed out, however, that a very remarkable new idea, namely, the asymptotic expansion of the heat invariants $a_k(p,r)$ defined on geodesic spheres, $S_p(r)$, is introduced in the paper. It can be used for developing both geometric uncertainty theory and global vs. local spectral investigations. Among my contributions to this developing field is the following statement: Average volumes, $\int vol(B_p(r))dp$ resp. $\int vol(S_p(r))dp$, of geodesic balls resp. spheres are generically not determined by the spectra of compact Riemann manifolds. This theorem interestingly contrasts the statement asserting that the volume of the whole manifold can be determined in terms of this global spectrum. We also have: Music written for local drums can not be played, in general, on the whole manifold., 48 pages. Exposition improved. New constructions are also described which reprove that the local symmetry on harmonic manifolds can not be determined by the spectra of local geodesic balls

In this paper such Riemann metrics are established whose Laplace-Beltrami operators are identical to familiar Hamilton operators of elementary particle systems. Such metrics are the natural positive definite invariant metrics defined on two-step nilpotent Lie groups. The corresponding wave and Schroedinger operators emerge in the Laplacians of the static resp. solvable extensions of these nilpotent groups. The latter manifolds are endowed with natural invariant indefinite metric of Lorentz signature. Thus, these new exact mathematical models provide a relativistic theory for elementary particles. On the solvable extensions these models look like Friedmann's expanding universe being adopted to the microscopic level. Like the macroscopic one, also these microscopic expanding models obey Hubble's law. The microscopic models, however, offer much more complex structures with much more subtle explanations for some of those phenomena which have originally been clarified by the Friedmann model. One of the most important new features of this theory is that the electromagnetic, the weak-nuclear, and the strong-nuclear forces emerge in a unified way., Comment: submitted

Cooperative movements assured economic welfare of villages, led them to the way of becoming real citizens in the first half of the XXth century. By that period we can say that for improving competitivity advancing coops, and their social role is necessary. In an active coop continuous modernization is needed. This is due to global challenges and multinational companies, and also smaller dominant ones. This is why Hangya cooperative organisations are to be remembered for being the first in the Carpatian basin from the late 19th century. Manufacturers can realize their interests by building their own organizations. This is the cooperation of separate farmers, today dealing with very complicated transnational organizations. Realizing these may be the way to improve livings in the countryside, especially in the agriculture. Joining the following forms of groups is a unique and necessary way to reach these. By this the conclusion is: there must be an integrated network system for production branches controlled by coops with cooperative tenets in Transylvania. For this historical examples of helping farmers remain separate, reach markets must be known and adopted into today’s circumstances.

Munkámban Debrecen városmarketing-csoportjának tevékenységét vizsgáltam. Az általuk megjelölt három legfontosabb célcsoport igényeit térképeztem fel kvalitatív módszerrel, megvizsgálva ezzel, hogy a célcsoportok által igényelt intézkedések és a városmarketing segítségével kijelölt fejlesztési célok mennyiben fedik egymást. Megállapítottam, hogy a debreceni városmarketing-csoport évről-évre egyre kiforrottabb, egységes szemléletű, átgondolt marketinget valósít meg, de ennek ellenére jelentős erőfeszítések szükségesek a regionális szerep elérése, a helyzet részletes feltárása és a célcsoportokkal folytatott kommunikáció javítása érdekében. - My work examines the activities of Debrecen’s city-marketing group. Using a qualitative method I mapped the requirements of the three most important target groups they identified, thereby investigating the extent to which the measures required by the target groups overlap with the development goals highlighted with the help of the city-marketing group. I discovered that, year on year, the Debrecen city-marketing group implements increasingly mature, thoughtful marketing with a unified approach, despite which however, significant efforts are still required in the interests of achieving a regional role, of uncovering the situation in detail, and of improving communication with the target groups.

Recently, several algorithms have been proposed for independent subspace analysis where hidden variables are i.i.d. processes. We show that these methods can be extended to certain AR, MA, ARMA and ARIMA tasks. Central to our paper is that we introduce a cascade of algorithms, which aims to solve these tasks without previous knowledge about the number and the dimensions of the hidden processes. Our claim is supported by numerical simulations. As a particular application, we search for subspaces of facial components., Comment: 9 pages, 2 figures

By a recent observation, the Laplacians on the Riemannian manifolds the author used for isospectrality constructions are nothing but the Zeeman-Hamilton operators of free charged particles. These manifolds can be considered as prototypes of the so called Zeeman manifolds. This observation allows to develop a spectral theory both on open Z-manifolds and their compact submanifolds. The theory on open manifolds leads to a new nonperturbative approach to the infinities of QED. This idea exploits that the quantum Hilbert space decomposes into subspaces (Zeeman zones) which are invariant under the actions both of this Zeeman-Laplace operator and the natural complex Heisenberg group representation. Thus a well defined particle theory and zonal geometry can be developed on each zone separately. The most surprising result is that quantities divergent on the global setting are finite on the zonal setting. Even the zonal Feynman integral is well defined. The results include explicit computations of objects such as the zonal spectra, the waves defining the zonal point-spreads, the zonal Wiener-Kac resp. Dirac-Feynman flows, and the corresponding partition functions. The observation adds new view-point also to the problem of finding intertwining operators by which isospectral pairs of metrics with different local geometries on compact submanifolds can be constructed. Among the examples the author constructed the most surprising are the isospectrality families containing both homogeneous and locally inhomogeneous metrics. The observation provides even quantum physical interpretation to the isospectrality., Comment: 21 pages, presented at CUNY's Geometric Analysis Conference, February 3-5, 2006, http://math.gc.cuny.edu/conferences/conferences.html

In this paper we give a necessary combinatorial condition for a negative--definite plumbing tree to be suitable for rational blow--down, or to be the graph of a complex surface singularity which admits a rational homology disk smoothing. New examples of surface singularities with rational homology disk smoothings are also presented; these include singularities with resolution graph having valency four nodes., Comment: 61 pages, 28 figures

We review the construction of Heegaard Floer homology for closed three-manifolds and also for knots and links in the three-sphere. We also discuss three applications of this invariant to knot theory: studying the Thurston norm of a link complement, the slice genus of a knot, and the unknotting number of a knot. We emphasize the application to the Thurston norm, and illustrate the theory in the case of the Conway link., Comment: To appear in the Proceedings for ICM-2006 Madrid

Here, a separation theorem about Independent Subspace Analysis (ISA), a generalization of Independent Component Analysis (ICA) is proven. According to the theorem, ISA estimation can be executed in two steps under certain conditions. In the first step, 1-dimensional ICA estimation is executed. In the second step, optimal permutation of the ICA elements is searched for. We present sufficient conditions for the ISA Separation Theorem. Namely, we shall show that (i) elliptically symmetric sources, (ii) 2-dimensional sources invariant to 90 degree rotation, among others, satisfy the conditions of the theorem., Comment: 11 pages, 0 figures

In Hungary the amount of money spent on wine marketing is much below the level as it should be and the amounts spent are largely to support direct selling. Choosing the right distribution channel is of key importance. My objective was to identify wine buying behavior of consumers in the hypermarket. I have chosen this type of distribution channel because it is the fastest growing one in Hungary and the largest in wine trade and compared to the international situation it plays a leading role. In the article I show the results of analyzing 578 questionnaires. According to the research fou r wine buyer segments were to identify the 'Drinking with friends', the 'Trendy guests', the 'Cognoscente', and the 'Average friends of wine'. These segments are clearly to distinguish from each other and can help the wine producers and the hypermarket itself to set up such marketing plans and strategies that creates higher satisfaction of the wine buyers.

We construct an infinite family of simply connected, pairwise nondiffeomorphic 4-manifolds, all homeomorphic to 3CP^2 blown up at 9 points., Comment: 7 pages

Motivated by a construction of Fintushel and Stern, we show that the topological 4--manifold $CP^2#5{\bar CP^2}$ supports infinitely many distinct smooth structures., Comment: 14 pages, 4 figures; details of computation of Seiberg-Witten invariants is added

Consuming habits have very much changed in Hungary in the last decades after the transformation. To get everything at the same place got bigger importance. According to this influence big super and hypermarkets have been created and shopping centres came alive. These days it is very important to realise what the consumers want and to understand they motives. My objective was to get to know consumer habits and wine consuming habits in hypermarkets and to compare a West European hypermarket with one Central Eastern European country after the transformation in order to realise similarities and differences and if possible some conclusions to the future of these kind of distribution channels in CEE countries. The other important part of the research was to get information about people's opinion about the hypermarket and to realise the more important influencing factors in their preference scale. These researches were made in the Netherlands at the A&P Hypermarket chain in 2000. During the questionnaire researches I asked 118-118 people and in Hungary at Cora Hypermarkets in 2002 where 170 people were questioned. In my opinion people gave a lot of very important information to the hypermarket chains with highlighting weak and strong points.

Given a contact structure on a closed, oriented three-manifold $Y$, we describe an invariant which takes values in the three-manifold's Floer homology $\HFa$. This invariant vanishes for overtwisted contact structures and is non-zero for Stein fillable ones. The construction uses of Giroux's interpretation of contact structures in terms of open book decompositions, and the knot Floer homologies introduced in math.GT/0209056., Comment: 22 pages, 3 figures

In an earlier paper, we introduced a knot invariant for a null-homologous knot K in an oriented three-manifold Y, which is closely related to the Heegaard Floer homology of Y. In this paper we investigate some properties of these knot homology groups for knots in the three-sphere. We give a combinatorial description for the generators of the chain complex and their gradings. With the help of this description, we determine the knot homology for alternating knots, showing that in this special case, it depends only on the signature and the Alexander polynomial of the knot (generalizing a result of Rasmussen for two-bridge knots). Applications include new restrictions on the Alexander polynomial of alternating knots., Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper6.abs.html

In an earlier paper (math.SG/0101206), we introduced Floer homology theories associated to closed, oriented three-manifolds Y and SpinC structures. In the present paper, we give calculations and study the properties of these invariants. The calculations suggest a conjectured relationship with Seiberg-Witten theory. The properties include a relationship between the Euler characteristics of these theories and Turaev's torsion, a relationship with the minimal genus problem (Thurston norm), and surgery exact sequences. We also include some applications of these techniques to three-manifold topology., Comment: 87 pages, 12 figures. To appear in Annals of Mathematics. Reorganized both this paper and its prequel, math.SG/0101206

The aim of this article is to introduce invariants of oriented, smooth, closed four-manifolds, built using the Floer homology theories defined in two earlier papers (math.SG/0101206 and math.SG/0105202). This four-dimensional theory also endows the corresponding three-dimensional theories with additional structure: an absolute grading of certain of its Floer homology groups. The cornerstone of these constructions is the study of holomorphic disks in the symmetric products of Riemann surfaces., Comment: 73 pages, 6 figures

We use Heegaard decompositions and the theta divisor on a Riemannian surface to define a three-manifold invariant for rational homology three-spheres. This invariant is defined on the set of $Spin^c$ structures $$ {\hat \theta}\colon Spin^c(Y)\longrightarrow Q. $$ In the first part of the paper, we give the definition of the invariant (which builds on the theory developed in the article, "The theta divisor and three-manifold invariants"). In the second part, we establish a relationship between this invariant and the Casson-Walker invariant., Comment: 50 pages, 3 figures

In this paper we study an invariant for oriented three-manifolds with $b_1>0$, which is defined using Heegaard splittings and the theta divisor of a Riemann surface. The paper is divided into two parts, the first of which gives the definition of the invariant, and the second of which identifies it with more classical (torsion) invariants of three-manifolds. Its close relationship with Seiberg-Witten theory is also addressed., 51 pages; 1 figure

Fullerenes have attracted considerable attention in different fields of science since their discovery in 1985. Investigations of physical, chemical and biological properties of fullerenes have yielded promising information. It is inferred that size, hydrophobicity, three-dimensionality and electronic configurations make them an appealing subject in medicinal chemistry. Their unique carbon cage structure coupled with immense scope for derivatization make them a potential therapeutic agent. The study of biological applications has attracted increasing attention despite the low solubility of carbon spheres in physiological media. The fullerene family, and especially C60, has appealing photo, electrochemical and physical properties, which can be exploited in various medical fields. Fullerene is able to fit inside the hydrophobic cavity of HIV proteases, inhibiting the access of substrates to the catalytic site of enzyme. It can be used as radical scavenger and antioxidant. At the same time, if exposed to light, fullerene can produce singlet oxygen in high quantum yields. This action, together with direct electron transfer from excited state of fullerene and DNA bases, can be used to cleave DNA. In addition, fullerenes have been used as a carrier for gene and drug delivery systems. Also they are used for serum protein profiling as MELDI material for biomarker discovery. In this review we report the aspects of medicinal applications of fullerenes.

We propose a novel adaptive test of goodness-of-fit, with computational cost linear in the number of samples. We learn the test features that best indicate the differences between observed samples and a reference model, by minimizing the false negative rate. These features are constructed via Stein's method, meaning that it is not necessary to compute the normalising constant of the model. We analyse the asymptotic Bahadur efficiency of the new test, and prove that under a mean-shift alternative, our test always has greater relative efficiency than a previous linear-time kernel test, regardless of the choice of parameters for that test. In experiments, the performance of our method exceeds that of the earlier linear-time test, and matches or exceeds the power of a quadratic-time kernel test. In high dimensions and where model structure may be exploited, our goodness of fit test performs far better than a quadratic-time two-sample test based on the Maximum Mean Discrepancy, with samples drawn from the model., Comment: Accepted to NIPS 2017