stable pairs and the homfly polynomial given a planar curve singularity we prove a conjecture of oblomkov shende relating the geometry of its hilbert scheme of points to the homfly polynomial of the associated algebraic link more generally we prove an extension of this conjecture due to diaconescu hua soibelman relating stable pair invariants on the conifold to the colored homfly polynomial of the algebraic link our proof uses wall crossing techniques to prove a blowup identity on the algebro geometric side we prove a matching identity for the colored homfly polynomials of a link using skein theoretic techniques

configurations in abelian categories ii ringel hall algebras abstract this is the second in a series on configurations in an abelian category a given a finite poset i an i configuration is a finite collection of objects j and morphisms j k or j k j k in a satisfying some axioms where j k i configurations describe how an object x in a decomposes into subobjects the first paper defined configurations and studied moduli spaces of i configurations in a using the theory of artin stacks it showed well behaved moduli stacks obj a m i a of objects and configurations in a exist when a is the abelian category coh p of coherent sheaves on a projective scheme p or mod k q of representations of a quiver q write cf obj a for the vector space of q valued constructible functions on the stack obj a motivated by the idea of ringel hall algebras we define an associative multiplication on cf obj a using pushforwards and pullbacks along 1 morphisms between configuration moduli stacks so that cf obj a is a q algebra we also study representations of cf obj a the lie subalgebra cf ind obj a of functions supported on indecomposables and other algebraic structures on cf obj a then we generalize all these ideas to stack functions sf obj a a universal generalization of constructible functions containing more information when ext i x y 0 for all x y a and i 1 or when a coh p for p a calabi yau 3 fold we construct lie algebra morphisms from stack algebras to explicit algebras which will be important in the sequels on invariants counting semistable objects in a

gopakumar vafa invariants via vanishing cycles in this paper we propose an ansatz for defining gopakumar vafa invariants of calabi yau threefolds using perverse sheaves of vanishing cycles our proposal is a modification of a recent approach of kiem li which is itself based on earlier ideas of hosono saito takahashi we conjecture that these invariants are equivalent to other curve counting theories such as gromov witten theory and pandharipande thomas theory our main theorem is that for local surfaces our invariants agree with pt invariants for irreducible one cycles we also give a counter example to the kiem li conjectures where our invariants match the predicted answer finally we give examples where our invariant matches the expected answer in cases where the cycle is non reduced non planar or non primitive

curve counting via stable pairs in the derived category for a nonsingular projective 3 fold x we define integer invariants virtually enumerating pairs c d where c x is an embedded curve and d c is a divisor a virtual class is constructed on the associated moduli space by viewing a pair as an object in the derived category of x the resulting invariants are conjecturally equivalent after universal transformations to both the gromov witten and dt theories of x for calabi yau 3 folds the latter equivalence should be viewed as a wall crossing formula in the derived category

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

how to stretch and shrink vowel systems results from a vowel normalization procedure one of the goals of phonetic investigations is to find strategies for vowel production independent of speaker specific vocal tract anatomies and individual biomechanical properties in this study techniques for speaker normalization that are derived from procrustes methods were applied to acoustic and articulatory data more precisely data consist of the first two formants and emma fleshpoint markers of stressed and unstressed vowels of german from seven speakers in the consonantal context t main results indicate that a for the articulatory data the normalization can be related to anatomical properties palate shapes b the recovery of phonemic identity is of comparable quality for acoustic and articulatory data c the procedure outperforms the lobanov transform in the acoustic domain in terms of phoneme recovery and d this advantage comes at the cost of partly also changing ellipse orientations which is in accordance with the formulation of the algorithms

an introduction to motivic hall algebras abstract we give an introduction to joyce s construction of the motivic hall algebra of coherent sheaves on a variety m when m is a calabi yau threefold we define a semi classical integration map from a poisson subalgebra of this hall algebra to the ring of functions on a symplectic torus this material will be used in bridgeland 2011 3 to prove some basic properties of donaldson thomas curve counting invariants on calabi yau threefolds

acoustic articulatory mapping in vowels by locally weighted regression a method for mapping between simultaneously measured articulatory and acoustic data is proposed the method uses principal components analysis on the articulatory and acoustic variables and mapping between the domains by locally weighted linear regression or loess cleveland w s 1979 j am stat assoc 74 829 836 the latter method permits local variation in the slopes of the linear regression assuming that the function being approximated is smooth the methodology is applied to vowels of four speakers in the wisconsin x ray microbeam speech production database with formant analysis results are examined in terms of 1 examples of forward articulation to acoustics mappings and inverse mappings 2 distributions of local slopes and constants 3 examples of correlations among slopes and constants 4 root mean square error and 5 sensitivity of formant frequencies to articulatory change it is shown that the results are qualitatively correct and that loess performs better than global regression the forward mappings show different root mean square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings at least for the data chosen for the current study some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented

cusps of the kahler moduli space and stability conditions on k3 surfaces ma int j math 20 6 727 750 2009 established a bijection between fourier mukai partners of a k3 surface and cusps of the kahler moduli space the kahler moduli space can be described as a quotient of bridgeland s stability manifold we study the relation between stability conditions near to a cusp and the associated fourier mukai partner y in the following ways 1 we compare the heart of to the heart of coherent sheaves on y 2 we construct y as moduli space of stable objects an appendix is devoted to the group of auto equivalences of mathcal d b x which respect the component stab dagger x of the stability manifold

higher dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed nilsson oscillator abstract based on the riemann and caputo definitions of the fractional derivative we use the fractional extensions of the standard rotation group s o 3 to construct a higher dimensional representation of a fractional rotation group with mixed derivative types an extended symmetric rotor model is derived which predicts the sequence of magic proton and neutron numbers accurately the ground state properties of nuclei are correctly reproduced within the framework of this model

the donaldson thomas invariants under blowups and flops using the degeneration formula for doanldson thomas invariants we proved formulae for blowing up a point and simple flops given a smooth projective calabi yau 3 fold x the moduli space of stable sheaves on x has virtual dimension zero donaldson and thomas d t defined the holomorphic casson invariant of x which essentially counts the number of sta ble bundles on x however the moduli space has positive dimension and is singular in general making use of virtual cycle technique see b f and l t thomas showed in thomas that one can define a virtual moduli cycle for some x including calabi yau and fano 3 folds as a consequence one can define donaldson type in variants of x which are deformation invariant donaldson thomas invariants pro vide a new vehicle to study the geometry and other aspects of higher dimensional varieties it is important to understand these invariants much studied gromov witten invariants of x are the counting of stable maps from curves to x in mnop1 mnop2 maulik nekrasov okounkov and pandharipande discovered relations between gromov witten invarints of x and donaldson thomas invariants constructed from moduli spaces of ideal sheaves of curves on x they conjectured that these two invariants can be identified via the equations of partition functions of both theory this suggests that many phe nomena on gromov witten theory have the counterparts in donaldson thomas theory donaldson thomas invariants are deformation independent in the birational geometry of 3 folds we have blowups and flops donaldson thomas invariants couldn t be effective in studying birational geometry unless we understand how invariants change under birational operations li and ruan in l r studied how gromov witten invariants change under a flop for calabi yau 3 fold they proved that one can identify the 3 point functions of x and the flop x f of x up to some transformation of the q variables the same question was aslo studied by liu and yau in l y recently using the j li s degeneration formula from algebraic geometry in hu1 hu2 the first author studied the change of gromov witten

a characterization of rational singularities is given bythe reynolds operator a well known and widely used theoremstates that in characteristic 0 canonicalsingularities are cohen macaulay and therefore rational see e and kmm the original proofs are based on a very clever use of grothendieck duality simulta neously for a resolution and its restriction onto the exceptional divisor and on a doubleloop induction kollar gave a simpler proof in k2 11 without using derived cate gories but still relying on a technically hard vanishing theorem recently kollar andmori found a simple proof allowing nonempty boundaries they do not use derivedcategories either but restrict to the projective case see km 5 18 these proofs areingenious but one would like to have a simple natural proof at least in the classical case when the boundary is empty as an application of theorem1 a simple proof is given here in the classical case but without the projective assumption this proof seems even simpler than that ofkollar and mori derived categories and grothendieck duality are used but in sucha simple way that one is tempted to say that this proof is the most natural one notealso that everything used here was already available when the question was raised forthe rst time a statement similar to theorem 1 was given in k2 3 12 some ideas of the

configurations in abelian categories iii stability conditions and identities this is the third in a series on configurations in an abelian category given a finite poset i an i configuration s p is a finite collection of objects s j and morphisms j k or in satisfying some axioms where j k are subsets of i configurations describe how an object x in decomposes into subobjects the first paper defined configurations and studied moduli spaces of configurations in using the theory of artin stacks it showed well behaved moduli stacks of objects and configurations in exist when is the abelian category coh p of coherent sheaves on a projective scheme p or of representations of a quiver q the second studied algebras of constructible functions and stack functions on this paper introduces weak stability conditions t t on we show the moduli spaces of t semistable indecomposable t semistable and t stable objects in class a are constructible sets in and some associated configuration moduli spaces constructible in so their characteristic functions and are constructible we prove many identities relating these constructible functions and their stack function analogues under pushforwards we introduce interesting algebras of constructible and stack functions and study their structure in the fourth paper we show are independent of t t and construct invariants of

fractional phase transition in medium size metal clusters abstract based on the riemann and caputo definition of the fractional derivative we use the fractional extensions of the standard rotation group s o 3 to construct a higher dimensional representation of a fractional rotation group with mixed derivative types an analytic extended symmetric rotor model is derived which correctly predicts the sequence of magic numbers in metal clusters it is demonstrated that experimental data may be described by assuming a sudden change in the fractional derivative parameter which is interpreted as a second order phase transition in the region of cluster size with 200 n 300

relationship between tongue positions and formant frequencies in female speakers this study examined the relationship 1 between acoustic vowel space and the corresponding tongue kinematic vowel space and 2 between formant frequencies f1 and f2 and tongue x y coordinates for the same time sampling point thirteen healthy female adults participated in this study electromagnetic articulography and synchronized acoustic recordings were utilized to obtain vowel acoustic and tongue kinematic data across ten speech tasks intra speaker analyses showed that for 10 of the 13 speakers the acoustic vowel space was moderately to highly correlated with tongue kinematic vowel space much weaker correlations were obtained for inter speaker analyses correlations of individual formants with tongue positions showed that f1 varied strongly with tongue position variations in the y dimension whereas f2 was correlated in equal magnitude with variations in the x and y positions for within speaker analyses the size of the acoustic vowel space is likely to provide a reasonable inference of size of the tongue working space for most speakers unfortunately there is no a priori obvious way to identify the speakers for whom the covariation is not significant a second conclusion is that f1 variations reflect tongue height but f2 is a much more complex reflection of tongue variation in both dimensions

three dimensional flops and noncommutative rings limburgs univ ctr dept math b 3590 diepenbeek belgium van den bergh m limburgs univ ctr dept math univ campus b 3590 diepenbeek belgium vdbergh luc ac be

common aspects of q deformed lie algebras and fractional calculus fractional calculus and q deformed lie algebras are closely related both concepts expand the scope of standard lie algebras to describe generalized symmetries a new class of fractional q deformed lie algebras is proposed which for the first time allows a smooth transition between different lie algebras for the fractional harmonic oscillator the corresponding fractional q number is derived it is shown that the resulting energy spectrum is an appropriate tool to describe e g the ground state spectra of even even nuclei in addition the equivalence of rotational and vibrational spectra for fractional q deformed lie algebras is shown and the b e2 values for the fractional q deformed symmetric rotor are calculated a first interpretation of half integer representations of the fractional rotation group is given in terms of a description of k 1 2 band spectra of odd even nuclei