The Lambek calculus with iteration: two variants

Formulae of the Lambek calculus are constructed using three binary connectives, multiplication and two divisions. We extend it using a unary connective, positive Kleene iteration. For this new operation, following its natural interpretation, we present two lines of calculi. The first one is a fragment of infinitary action logic and includes an omega-rule for introducing iteration to the antecedent. We also consider a version with infinite (but finitely branching) derivations and prove equivalence of these two versions. In Kleene algebras, this line of calculi corresponds to the *-continuous case. For the second line, we restrict our infinite derivations to cyclic (regular) ones. We show that this system is equivalent to a variant of action logic that corresponds to general residuated Kleene algebras, not necessarily *-continuous. Finally, we show that, in contrast with the case without division operations (considered by Kozen), the first system is strictly stronger than the second one. To prove this, we use a complexity argument. Namely, we show, using methods of Buszkowski and Palka, that the first system is $\Pi_1^0$-hard, and therefore is not recursively enumerable and cannot be described by a calculus with finite derivations

A Bragg glass phase in the vortex lattice of a type II superconductor

Although crystals are usually quite stable, they are sensitive to a disordered environment: even an infinitesimal amount of impurities can lead to the destruction of the crystalline order. The resulting state of matter has been a longstanding puzzle. Until recently it was believed to be an amorphous state in which the crystal would break into crystallites. But a different theory predicts the existence of a novel phase of matter: the so-called Bragg glass, which is a glass and yet nearly as ordered as a perfect crystal. The lattice of vortices that can contain magnetic flux in type II superconductors provide a good system to investigate these ideas. Here we show that neutron diffraction data of the vortex lattice in type II superconductors provides unambiguous evidence for a weak, power-law decay of the crystalline order characteristic of a Bragg glass. The theory also predicts accurately the electrical transport properties of superconductors; it naturally explains the observed phase transition and the dramatic jumps in the critical current associated with the melting of the Bragg glass. Moreover the model explains experiments as diverse as X-ray scattering in disordered liquid crystals and conductivity of electronic crystals.Comment: 9 pages, 4 figure

Leading particles and diffractive spectra in the Interacting Gluon Model

We discuss the leading particle spectra and diffractive mass spectra from the novel point of view, namely by treating them as particular examples of the general energy flow phenomena taking place in the multiparticle production processes. We argue that they show a high degree of universality what allows for their simple description in terms of the Interacting Gluon Model developed by us some time ago.Comment: Presented at Diffraction2002, Alushta, Crimea (Ukraina), August 31 - September 5, 2002. To be published by Kluwer Academic Publishers (2003) (necessary style files attached). Rewritten according to the Kluwer specification

Two-dimensional Vortices in Superconductors

Superconductors have two key characteristics. They expel magnetic field and they conduct electrical current with zero resistance. However, both properties are compromised in high magnetic fields which can penetrate the material and create a mixed state of quantized vortices. The vortices move in response to an electrical current dissipating energy which destroys the zero resistance state\cite{And64}. One of the central problems for applications of high temperature superconductivity is the stabilization of vortices to ensure zero electrical resistance. We find that vortices in the anisotropic superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi-2212) have a phase transition from a liquid state, which is inherently unstable, to a two-dimensional vortex solid. We show that at high field the transition temperature is independent of magnetic field, as was predicted theoretically for the melting of an ideal two-dimensional vortex lattice\cite{Fis80,Gla91}. Our results indicate that the stable solid phase can be reached at any field as may be necessary for applications involving superconducting magnets\cite{Has04,Sca04,COHMAG}. The vortex solid is disordered, as suggested by previous studies at lower fields\cite{Lee93,Cub93}. But its evolution with increasing magnetic field displays unexpected threshold behavior that needs further investigation.Comment: 5 pages and 4 figures. submitted to Nature Physic

Climate Change and invasibility of the Antarctic benthos

Benthic communities living in shallow-shelf habitats in Antarctica (<100-m depth) are archaic in their structure and function. Modern predators, including fast-moving, durophagous (skeleton-crushing) bony fish, sharks, and crabs, are rare or absent; slow-moving invertebrates are the top predators; and epifaunal suspension feeders dominate many soft substratum communities. Cooling temperatures beginning in the late Eocene excluded durophagous predators, ultimately resulting in the endemic living fauna and its unique food-web structure. Although the Southern Ocean is oceanographically isolated, the barriers to biological invasion are primarily physiological rather than geographic. Cold temperatures impose limits to performance that exclude modern predators. Global warming is now removing those physiological barriers, and crabs are reinvading Antarctica. As sea temperatures continue to rise, the invasion of durophagous predators will modernize the shelf benthos and erode the indigenous character of marine life in Antarctica

Assessment of potential cardiotoxic side effects of mitoxantrone in patients with multiple sclerosis

Previous studies showed that mitoxantrone can reduce disability progression in patients with multiple sclerosis (MS). There is, however, concern that it may cause irreversible cardiomyopathy with reduced left ventricular (LV) ejection fraction (EF) and congestive heart failure. The aim of this prospective study was to investigate cardiac side effects of mitoxantrone by repetitive cardiac monitoring in MS patients. The treatment protocol called for ten courses of a combined mitoxantrone (10 mg/m(2) body surface) and methylprednisolone therapy. Before each course, a transthoracic echocardiogram was performed to determine the LV end-diastolic diameter, the end-systolic diameter and the fractional shortening; the LV-EF was calculated. Seventy-three patients participated (32 males; age 48 +/- 12 years, range 20-75 years; 25 with primary progressive, 47 with secondary progressive and 1 with relapsing-remitting MS) who received at least four courses of mitoxantrone. Three of the 73 patients were excluded during the study (2 patients discontinued therapy; 1 patient with a previous history of ischemic heart disease developed atrial fibrillation after the second course of mitoxantrone). The mean cumulative dose of mitoxantrone was 114.0 +/- 33.8 mg. The mean follow-up time was 23.4 months (range 10-57 months). So far, there has been no significant change in any of the determined parameters (end-diastolic diameter, end-systolic diameter, fractional shortening, EF) over time during all follow-up investigations. Mitoxantrone did not cause signs of congestive heart failure in any of the patients. Further cardiac monitoring is, however, needed to determine the safety of mitoxantrone after longer follow-up times and at higher cumulative doses. Copyright (C) 2005 S. Karger AG, Basel

Modelling stereotyping in cooperation systems

Cooperation is a sophisticated example of collective intelligence. This is particularly the case for indirect reciprocity, where benefit is provided to others without a guarantee of a future return. This is becoming increasingly relevant to future technology, where autonomous machines face cooperative dilemmas. This paper addresses the problem of stereotyping, where traits belonging to an individual are used as proxy when assessing their reputation. This is a cognitive heuristic that humans frequently use to avoid deliberation, but can lead to negative societal implications such as discrimination. It is feasible that machines could be equally susceptible. Our contribution concerns a new and general framework to examine how stereotyping affects the reputation of agents engaging in indirect reciprocity. The framework is flexible and focuses on how reputations are shared. This offers the opportunity to assess the interplay between the sharing of traits and the cost, in terms of reduced cooperation, through opportunities for shirkers to benefit. This is demonstrated using a number of key scenarios. In particular, the results show that cooperation is sensitive to the structure of reputation sharing between individuals

The Role of Anorexia in Resistance and Tolerance to Infections in Drosophila

Infections initiate a signaling loop in which sick animals become anorexic, and the resulting change in diet alters the body's ability to fight infections in good and bad ways

Dietary Acrylamide Intake and the Risk of Lymphatic Malignancies: The Netherlands Cohort Study on Diet and Cancer

BACKGROUND: Acrylamide, a probable human carcinogen, is present in many everyday foods. Since the finding of its presence in foods in 2002, epidemiological studies have found some suggestive associations between dietary acrylamide exposure and the risk of various cancers. The aim of this prospective study is to investigate for the first time the association between dietary acrylamide intake and the risk of several histological subtypes of lymphatic malignancies. METHODS: The Netherlands Cohort Study on diet and cancer includes 120,852 men and women followed-up since September 1986. The number of person years at risk was estimated by using a random sample of participants from the total cohort that was chosen at baseline (n =5,000). Acrylamide intake was estimated from a food frequency questionnaire combined with acrylamide data for Dutch foods. Hazard ratios (HRs) were calculated for acrylamide intake as a continuous variable as well as in categories (quintiles and tertiles), for men and women separately and for never-smokers, using multivariable-adjusted Cox proportional hazards models. RESULTS: After 16.3 years of follow-up, 1,233 microscopically confirmed cases of lymphatic malignancies were available for multivariable-adjusted analysis. For multiple myeloma and follicular lymphoma, HRs for men were 1.14 (95% CI: 1.01, 1.27) and 1.28 (95% CI: 1.03, 1.61) per 10 µg acrylamide/day increment, respectively. For never-smoking men, the HR for multiple myeloma was 1.98 (95% CI: 1.38, 2.85). No associations were observed for women. CONCLUSION: We found indications that acrylamide may increase the risk of multiple myeloma and follicular lymphoma in men. This is the first epidemiological study to investigate the association between dietary acrylamide intake and the risk of lymphatic malignancies, and more research into these observed associations is warranted