Easiness Amplification and Uniform Circuit Lower Bounds

We present new consequences of the assumption that time-bounded algorithms can be "compressed" with non-uniform circuits. Our main contribution is an "easiness amplification" lemma for circuits. One instantiation of the lemma says: if n^{1+e}-time, tilde{O}(n)-space computations have n^{1+o(1)} size (non-uniform) circuits for some e > 0, then every problem solvable in polynomial time and tilde{O}(n) space has n^{1+o(1)} size (non-uniform) circuits as well. This amplification has several consequences: * An easy problem without small LOGSPACE-uniform circuits. For all e > 0, we give a natural decision problem, General Circuit n^e-Composition, that is solvable in about n^{1+e} time, but we prove that polynomial-time and logarithmic-space preprocessing cannot produce n^{1+o(1)}-size circuits for the problem. This shows that there are problems solvable in n^{1+e} time which are not in LOGSPACE-uniform n^{1+o(1)} size, the first result of its kind. We show that our lower bound is non-relativizing, by exhibiting an oracle relative to which the result is false. * Problems without low-depth LOGSPACE-uniform circuits. For all e > 0, 1 < d < 2, and e < d we give another natural circuit composition problem computable in tilde{O}(n^{1+e}) time, or in O((log n)^d) space (though not necessarily simultaneously) that we prove does not have SPACE[(log n)^e]-uniform circuits of tilde{O}(n) size and O((log n)^e) depth. We also show SAT does not have circuits of tilde{O}(n) size and log^{2-o(1)}(n) depth that can be constructed in log^{2-o(1)}(n) space. * A strong circuit complexity amplification. For every e > 0, we give a natural circuit composition problem and show that if it has tilde{O}(n)-size circuits (uniform or not), then every problem solvable in 2^{O(n)} time and 2^{O(sqrt{n log n})} space (simultaneously) has 2^{O(sqrt{n log n})}-size circuits (uniform or not). We also show the same consequence holds assuming SAT has tilde{O}(n)-size circuits. As a corollary, if n^{1.1} time computations (or O(n) nondeterministic time computations) have tilde{O}(n)-size circuits, then all problems in exponential time and subexponential space (such as quantified Boolean formulas) have significantly subexponential-size circuits. This is a new connection between the relative circuit complexities of easy and hard problems

Temporal aspects of digital games

Temporal issues related to digital games go beyond the strictly literary or film studies character of the description and implies technological and marketing issues. It can be outlined by referring to the concept of Andrzej Stoff, who analyzed the spatial dimension of the world of the novel (“delineating space”, “creating”, “functionalizing”, “valorising”). Relating these four detailed issues – constituting the basic subject of description, analysis and interpretation – to temporal aspects, it is appropriate to talk about measuring (conventionalizing, relativizing) time, thematizing, functionalizing and valorizing it. Taking into account the above categories, the most typical concretizations of temporal phenomena can be further defined: functional (classic chronometry, clock, server time, time of a running process), gameplay (real time, relativization, quest time, respawn time), thematic concretizations (e.g. retrospection as a compositional dominant of multimodal narratives) and marketing concretizations (commercialization of time).Temporal issues related to digital games go beyond the strictly literary or film studies character of the description and implies technological and marketing issues. It can be outlined by referring to the concept of Andrzej Stoff, who analyzed the spatial dimension of the world of the novel (“delineating space”, “creating”, “functionalizing”, “valorising”). Relating these four detailed issues – constituting the basic subject of description, analysis and interpretation – to temporal aspects, it is appropriate to talk about measuring (conventionalizing, relativizing) time, thematizing, functionalizing and valorizing it. Taking into account the above categories, the most typical concretizations of temporal phenomena can be further defined: functional (classic chronometry, clock, server time, time of a running process), gameplay (real time, relativization, quest time, respawn time), thematic concretizations (e.g. retrospection as a compositional dominant of multimodal narratives) and marketing concretizations (commercialization of time)

Production of relative clauses in monolingual Turkish children

Research on the production of relative clauses (RCs) has shown that in English, although children start using intransitive RCs at an earlier age, more complex, bi-propositional object RCs appear later (Hamburger & Crain, 1982; Diessel and Tomasello, 2005), and children use resumptive pronouns both in acceptable and unacceptable ways (McKee, McDaniel, & Snedeker, 1998; McKee & McDaniel, 2001). To date, it is unclear whether or not the same picture emerges in Turkish, a language with an SOV word-order and overt case marking. Some studies suggested that subject RCs are more frequent in adults and children (Slobin, 1986) and yield a better performance than object RCs (Özcan, 1996), but others reported the opposite pattern (Ekmekçi, 1990). Our study addresses this issue in Turkish children and adults, and uses participants’ errors to account for the emerging asymmetry between subject and object RCs. 37 5-to-8 year old monolingual Turkish children and 23 adult controls participated in a novel elicitation task involving cards, each consisting of four different pictures (see Figure 1). There were two sets of cards, one for the participant and one for the researcher. The former had animals with accessories (e.g., a hat) whereas the latter had no accessories. Participants were instructed to hold their card without showing it to the researcher and describe the animals with particular accessories. This prompted the use of subject and object RCs. The researcher had to identify the animals in her card (see Figure 2). A preliminary repeated measures ANOVA with the factor Group (pre-school, primary-school children) showed no differences between the groups in the use of RCs (p>.1), who were therefore collapsed into one for further analyses. A repeated measures ANOVA with the factors Group (children, adults) and RC-Type (Subject, Object) showed that children used fewer RCs than adults (F(1,58)=7.54, p<.01), and both groups used fewer object than subject RCs (F(1,58)=22.46, p<.001), but there was no Group by RC-Type interaction (see Figure 3). A similar ANOVA on the rate of grammatical RCs showed a main effect of Group (F(1,58)=77.25, p<.001), a main effect of RC-Type (F(1,58)=66.33, p<.001), and an interaction of Group by RC-Type (F(1,58)=64.6, p<.001) (see Figure 4). Children made more errors than adults in object RCs (F(1,58)=87.01, p<.001), and children made more errors in object compared to subject RCs (F(1,36)=106.35, p<.001), but adults did not show this asymmetry. The error analysis revealed that children systematically avoided the object-relativizing morpheme –DIK, which requires possessive agreement with the genitive-marked subject. They also used resumptive pronouns and resumptive full-DPs in the extraction site similarly to English children (see Figure 5). These findings are in line with Slobin (1986) and Özcan (1996). Children’s errors suggest that they avoid morphosyntactic complexity of object RCs and try to preserve the canonical word order by inserting resumptive pronouns in the extraction site. Finally, cross-linguistic similarity in the acquisition of RCs in typologically different languages suggests a higher accessibility of subject RCs both at the structural (Keenan and Comrie, 1977) and conceptual level (Bock and Warren, 1986)

The universality of polynomial time Turing equivalence

We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin's ultrafilter on the Turing degrees

Semi-relativistic description of quasielastic neutrino reactions and superscaling in a continuum shell model

The so-called semi-relativistic expansion of the weak charged current in powers of the initial nucleon momentum is performed to describe charge-changing, quasielastic neutrino reactions $(\nu_\mu,\mu^-)$ at intermediate energies. The quality of the expansion is tested by comparing with the relativistic Fermi gas model using several choices of kinematics of interest for ongoing neutrino oscillation experiments. The new current is then implemented in a continuum shell model together with relativistic kinematics to investigate the scaling properties of $(e,e')$ and $(\nu_\mu,\mu^-)$ cross sections.Comment: 33 pages, 10 figures, to appear in PR

Leibniz and the Problem of Temporary Truths

Not unlike many contemporary philosophers, Leibniz admitted the existence of temporary truths, true propositions that have not always been or will not always be true. In contrast with contemporary philosophers, though, Leibniz conceived of truth in terms of analytic containment: on his view, the truth of a predicative sentence consists in the analytic containment of the concept expressed by the predicate in the concept expressed by the subject. Given that analytic relations among concepts are eternal and unchanging, the problem arises of explaining how Leibniz reconciled one commitment with the other: how can truth be temporary, if concept-containment is not? This paper presents a new approach to this problem, based on the idea that a concept can be consistent at one time and inconsistent at another. It is argued that, given a proper understanding of what it is for a concept to be consistent, this idea is not as problematic as it may seem at first, and is in fact implied by Leibniz’s general views about propositions, in conjunction with the thesis that some propositions are only temporarily true

The Trinity and Extended Simples

In this paper, I will offer an analogy between the Trinity and extended simples that supports a Latin approach to the Trinity. The theoretical tools developed to discuss and debate extended simples in the literature of contemporary analytic metaphysics, I argue, can help us make useful conceptual distinctions in attempts to understand what it could be for God to be Triune. Furthermore, the analogy between extended simples and the Trinity might surprise some who find one of these at least plausibly possible and the other incoherent