Meron-Cluster Solution of Fermion and Other Sign Problems

Numerical simulations of numerous quantum systems suffer from the notorious sign problem. Important examples include QCD and other field theories at non-zero chemical potential, at non-zero vacuum angle, or with an odd number of flavors, as well as the Hubbard model for high-temperature superconductivity and quantum antiferromagnets in an external magnetic field. In all these cases standard simulation algorithms require an exponentially large statistics in large space-time volumes and are thus impossible to use in practice. Meron-cluster algorithms realize a general strategy to solve severe sign problems but must be constructed for each individual case. They lead to a complete solution of the sign problem in several of the above cases.Comment: 15 pages,LATTICE9

Meron-Cluster Simulation of a Chiral Phase Transition with Staggered Fermions

We examine a (3+1)-dimensional model of staggered lattice fermions with a four-fermion interaction and Z(2) chiral symmetry using the Hamiltonian formulation. This model cannot be simulated with standard fermion algorithms because those suffer from a very severe sign problem. We use a new fermion simulation technique - the meron-cluster algorithm - which solves the sign problem and leads to high-precision numerical data. We investigate the finite temperature chiral phase transition and verify that it is in the universality class of the 3-d Ising model using finite-size scaling.Comment: 21 pages, 6 figure

Semantics of nouns and nominal number

In the present paper, I will discuss the semantic structure of nouns and nominal number markers. In particular, I will discuss the question if it is possible to account for the syntactic and semantic formation of nominals in a parallel way, that is I will try to give a compositional account of nominal semantics. The framework that I will use is "twolevel semantics". The semantic representations and their type-theoretical basis will account for general cross-linguistic characteristics of nouns and nominal number and will show interdependencies between noun classes, number marking and cardinal constructions. While the analysis will give a unified account of bare nouns (like dog / water), it will distinguish between the different kinds of nominal terms (like a dog / dogs / water). Following the proposal, the semantic operations underlying the formation of the SR are basically the same for DPs as for CPs. Hence, from such an analysis, independent semantic arguments can be derived for a structural parallelism of nominals and sentences - that is, for the "sentential aspect" of noun phrases. I will first give a sketch of the theoretical background. I will then discuss the cross-linguistic combinatorial potential of nominal constructions, that is, the potential of nouns and number markers to combine with other elements and form complex expressions. This will lead to a general type-theoretical classification for the elements in question. In the next step, I will model the referential potential of nominal constructions. Together with the combinatorial potential, this will give us semantic representations for the basic elements involved in nominal constructions. In an overview, I will summarize our modeling of nouns and nominal number. I will then discuss in an outlook the "sentential aspect" of noun phrases

Did language give us numbers? : Symbolic thinking and the emergence of systematic numerical cognition

What role does language play in the development of numerical cognition? In the present paper I argue that the evolution of symbolic thinking (as a basis for language) laid the grounds for the emergence of a systematic concept of number. This concept is grounded in the notion of an infinite sequence and encompasses number assignments that can focus on cardinal aspects ("three pencils"), ordinal aspects ("the third runner"), and even nominal aspects ("bus #3"). I show that these number assignments are based on a specific association of relational structures, and that it is the human language faculty that provides a cognitive paradigm for such an association, suggesting that language played a pivotal role in the evolution of systematic numerical cognition

Dihedral Galois representations and Katz modular forms

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character \epsilon and weight k, where N is the conductor, \epsilon is the prime-to-p part of the determinant and k is the so-called minimal weight of \rho. In particular, k=1 if and only if \rho is unramified at p. Direct arguments are used in the exceptional cases, where general results on weight and level lowering are not available.Comment: 11 pages, LaTe

Removal of Carbamazepine from Drinking Water

Due to the increasing prevalence of prescription medication over the past few decades, pharmaceuticals have accumulated in various water sources. This has become a public health concern because many pharmaceuticals have limited research on the effects of chronic low-level exposure. According to the World’s Health Organization (WHO), traces of pharmaceuticals products have been reported in different water sources such as surface waters, wastewater, groundwater, and drinking water.[1] One pharmaceutical of interest that has been detected in water sources is carbamazepine. Carbamazepine is a common pharmaceutical prescribed for the treatment of seizure disorders, neuropathic pain, and various psychological disorders. It’s mechanism of action is “sodium channel blocking,” which is the impairment of conduction of sodium ions in sodium channels. This, in effect, reduces nervous-system conductivity in key areas related to the treated disorders mentioned above.[2] Carbamazepine is also not easily biodegradable and current conventional treatment methods in some drinking water and wastewater facilities do not adequately remove carbamazepine and other pharmaceuticals from treated water. While carbamazepine is not federally regulated by the Environmental Protection Agency (EPA) under the Safe Water Drinking Act (SWDA) at this time, it does have the potential for producing adverse health effects in humans. Therefore, being proactive in finding ways to remove carbamazepine and compounds like it should be encouraged. The Carbamaza-Clean team designed a bench scale unit as well as an in-home treatment system using granular activated carbon (GAC) to effectively remove carbamazepine from water. GAC was chosen for this design because it is inexpensive and does not create byproducts that are harmful to human health. Several experiments were conducted to determine the efficiency of the removal of carbamazepine using two different GACs: coconut shell GAC (CSGAC) and bituminous coal GAC (BGAC). A packed bed column was constructed to determine if both carbons could reduce the concentration of carbamazepine from 1 ppm to 1 ppb or lower. The CSGAC packed bed was able to lower the concentration below 1 ppb at a packed bed length of 4.4 ft, while the BGAC only required half that (2.2 ft). Both carbons can remove carbamazepine to the desired concentration; however, the costs vary. An economic analysis was performed to determine the costs of the carbons. The CSGAC system would cost $990 for the first year and$589.68 for each following year. The BGAC system would cost $639 for the first two years, and then$200 every two years following the initial capital investment

Predictive Processing and the Phenomenology of Time Consciousness: A Hierarchical Extension of Rick Grush’s Trajectory Estimation Model

This chapter explores to what extent some core ideas of predictive processing can be applied to the phenomenology of time consciousness. The focus is on the experienced continuity of consciously perceived, temporally extended phenomena (such as enduring processes and successions of events). The main claim is that the hierarchy of representations posited by hierarchical predictive processing models can contribute to a deepened understanding of the continuity of consciousness. Computationally, such models show that sequences of events can be represented as states of a hierarchy of dynamical systems. Phenomenologically, they suggest a more fine-grained analysis of the perceptual contents of the specious present, in terms of a hierarchy of temporal wholes. Visual perception of static scenes not only contains perceived objects and regions but also spatial gist; similarly, auditory perception of temporal sequences, such as melodies, involves not only perceiving individual notes but also slightly more abstract features (temporal gist), which have longer temporal durations (e.g., emotional character or rhythm). Further investigations into these elusive contents of conscious perception may be facilitated by findings regarding its neural underpinnings. Predictive processing models suggest that sensorimotor areas may influence these contents

Categories and paradigms : on underspecification in Russian declension

In morphological systems of the agglutinative type we sometimes encounter a nearly perfect one-to-one relation between form and function. Turkish inflectional morphology is, of course, the standard textbook example. Things seem to be quite different in systems of the flexive type. Declension in Contemporary Standard Russian (henceforth Russian, for short) may be cited as a typical example: We find, among other things, cumulative markers, “synonymous” endings (e.g., dative singular noun forms in -i, -e, or -u), and “homonymous” endings (e.g., -i, genitive, dative, and prepositional singular). True, some endings are more of an agglutinative nature, being bound to a specific case-number combination and applying across declensions, e.g., -am (dative plural, all nouns); and some cross the boundaries of word classes, e.g., -o, which serves as the nominative/accusative singular ending of neuter forms of pronouns (and adjectives) and as the nominative/accusative singular ending of (most) neuter nouns as well. Still, many observers have been struck by the impression that what we face here are rather uneconomic or even, so to speak, unnatural structures. But perhaps flexive systems are not as complicated as they seem. What seems to be uneconomic complexity may be, at least partially, an artifact of uneconomic descriptions

Are hedgehogs like pigs, or tortoises like toads? : language-specific effects of compound structure on conceptualisation

How far can language-specific structures influence conceptualisation? After a period of time where the discussion of any ‘Whorfian’ effects tended to be considered of little scientific merit, the recent decade has seen a renewed interest in this question. In particular, studies have aimed to tease apart ‘thinking for speaking’ from general cognition (cf. Slobin 1996, Stutterheim & Nüse 2002) and have shown that language-specific differences can often be observed in verbalisation as well as in the preverbal preparation phase of speech production, rather than in non-linguistic tasks

On projective linear groups over finite fields as Galois groups over the rational numbers

Ideas and techniques from Khare's and Wintenberger's article on the proof of Serre's conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups PSL_2(F_{l^r}) (for r running) occur as Galois groups over the rationals such that the corresponding number fields are unramified outside a set consisting of l, the infinite place and only one other prime.Comment: 7 pages, LaTeX; tiny change