scholarly journals Separation for dot-depth two

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Thomas Place ◽  
Marc Zeitoun
Keyword(s):  
Research Effort ◽  
First Language ◽  
Automata Theory ◽  
Open Problems ◽  
Third Language ◽  
First Order ◽  
Significant Research ◽  
Generic Construction ◽  
Low Levels ◽  
Special Case

The dot-depth hierarchy of Brzozowski and Cohen classifies the star-free languages of finite words. By a theorem of McNaughton and Papert, these are also the first-order definable languages. The dot-depth rose to prominence following the work of Thomas, who proved an exact correspondence with the quantifier alternation hierarchy of first-order logic: each level in the dot-depth hierarchy consists of all languages that can be defined with a prescribed number of quantifier blocks. One of the most famous open problems in automata theory is to settle whether the membership problem is decidable for each level: is it possible to decide whether an input regular language belongs to this level? Despite a significant research effort, membership by itself has only been solved for low levels. A recent breakthrough was achieved by replacing membership with a more general problem: separation. Given two input languages, one has to decide whether there exists a third language in the investigated level containing the first language and disjoint from the second. The motivation is that: (1) while more difficult, separation is more rewarding (2) it provides a more convenient framework (3) all recent membership algorithms are reductions to separation for lower levels. We present a separation algorithm for dot-depth two. While this is our most prominent application, our result is more general. We consider a family of hierarchies that includes the dot-depth: concatenation hierarchies. They are built via a generic construction process. One first chooses an initial class, the basis, which is the lowest level in the hierarchy. Further levels are built by applying generic operations. Our main theorem states that for any concatenation hierarchy whose basis is finite, separation is decidable for level one. In the special case of the dot-depth, this can be lifted to level two using previously known results.

scholarly journals Rainfall Infiltration Modeling: A Review

Water ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 1873 ◽  
Author(s):  
Renato Morbidelli ◽  
Corrado Corradini ◽  
Carla Saltalippi ◽  
Alessia Flammini ◽  
Jacopo Dari ◽  
...  
Keyword(s):  
Review Paper ◽  
Research Effort ◽  
Soil Characteristics ◽  
Rainfall Infiltration ◽  
Mathematical Representation ◽  
Open Problems ◽  
Significant Research ◽  
Complex Boundary ◽  
Definition Of ◽  
Horizontal Inhomogeneity

Infiltration of water into soil is a key process in various fields, including hydrology, hydraulic works, agriculture, and transport of pollutants. Depending upon rainfall and soil characteristics as well as from initial and very complex boundary conditions, an exhaustive understanding of infiltration and its mathematical representation can be challenging. During the last decades, significant research effort has been expended to enhance the seminal contributions of Green, Ampt, Horton, Philip, Brutsaert, Parlange and many other scientists. This review paper retraces some important milestones that led to the definition of basic mathematical models, both at the local and field scales. Some open problems, especially those involving the vertical and horizontal inhomogeneity of the soils, are explored. Finally, rainfall infiltration modeling over surfaces with significant slopes is also discussed.

scholarly journals Comprehension in English Medium Instruction (EMI) lectures: On the impact of lecturer L2 English use

2020 ◽  
Vol 10 (1) ◽  
pp. 73-91
Author(s):  
Joseph Siegel
Keyword(s):  
Teaching And Learning ◽  
First Language ◽  
Student Body ◽  
University Campuses ◽  
Student Comprehension ◽  
Teachers And Students ◽  
English Medium Instruction ◽  
Low Levels ◽  
Effectiveness And Efficiency ◽  
The Impact

AbstractThe importance and amount of English as a Lingua Franca (ELF) usage and English Medium Instruction (EMI) lectures continue to increase on university campuses as universities worldwide seek to promote internationalization among both the student body and the faculty. While EMI has become a priority, the teaching and learning that occurs within this framework needs to be monitored for effectiveness and efficiency. Many of the teachers and students in these EMI courses do not share a common first language and likely have a first language other than English. Therefore, they are operating in EMI with varying levels of second language (L2) English ability, which can lead to low levels of student comprehension, learning and satisfaction unless the lecturer takes special care in their delivery of content. This paper explores the linguistic composition of EMI lectures in the Swedish context and reports survey findings of students’ self-reported levels of comprehension related to lecture content and their lecturer’s L2 English use. Three case studies are described and illustrate various linguistic factors that can contribute to or inhibit student comprehension in EMI lectures. Pedagogic implications are presented with the intention of supporting EMI lecturers and their students.

Relativized realizability in intuitionistic arithmetic of all finite types

1978 ◽  
Vol 43 (1) ◽  
pp. 23-44 ◽  
Author(s):  
Nicolas D. Goodman
Keyword(s):  
Extension Theorem ◽  
General Notion ◽  
Conservative Extension ◽  
First Order ◽  
New Information ◽  
Reflection Theorem ◽  
Order Arithmetic ◽  
Special Case ◽  
Dependent Choice ◽  
Intuitionistic Arithmetic

In this paper we introduce a new notion of realizability for intuitionistic arithmetic in all finite types. The notion seems to us to capture some of the intuition underlying both the recursive realizability of Kjeene [5] and the semantics of Kripke [7]. After some preliminaries of a syntactic and recursion-theoretic character in §1, we motivate and define our notion of realizability in §2. In §3 we prove a soundness theorem, and in §4 we apply that theorem to obtain new information about provability in some extensions of intuitionistic arithmetic in all finite types. In §5 we consider a special case of our general notion and prove a kind of reflection theorem for it. Finally, in §6, we consider a formalized version of our realizability notion and use it to give a new proof of the conservative extension theorem discussed in Goodman and Myhill [4] and proved in our [3]. (Apparently, a form of this result is also proved in Mine [13]. We have not seen this paper, but are relying on [12].) As a corollary, we obtain the following somewhat strengthened result: Let Σ be any extension of first-order intuitionistic arithmetic (HA) formalized in the language of HA. Let Σω be the theory obtained from Σ by adding functionals of finite type with intuitionistic logic, intensional identity, and axioms of choice and dependent choice at all types. Then Σω is a conservative extension of Σ. An interesting example of this theorem is obtained by taking Σ to be classical first-order arithmetic.

Commitment in L3 relationships: Sacred vows or polyamory?

2021 ◽  
pp. 026765832098804
Author(s):  
David Stringer
Keyword(s):  
Second Language ◽  
First Language ◽  
Acquisition Process ◽  
Third Language ◽  
L3 Acquisition ◽  
Acquisition Device ◽  
Crosslinguistic Influence ◽  
The Mind ◽  
N Acquisition ◽  
Full Copy

Westergaard (2019) presents an updated account of the Linguistic Proximity Model and the micro-cue approach to the parser as an acquisition device. The property-by-property view of transfer inherent in this approach contrasts with other influential models that assume that third language (L3) acquisition involves the creation of a full copy of only one previously existing language in the mind. In this commentary, I review Westergaard’s proposal that first language (L1), second language (L2), and L3 acquisition proceed on the basis of incremental, conservative learning and her view of the parser as the engine of the acquisition process. I then provide several arguments in support of her position that crosslinguistic influence in L n acquisition may flow from any previously acquired language.

scholarly journals Systematic review of evidence underpinning non-pharmacological therapies in dementia

2018 ◽  
Vol 42 (4) ◽  
pp. 361 ◽  
Author(s):  
Richard Olley ◽  
Andrea Morales
Keyword(s):  
Systematic Review ◽  
Sleep Disturbances ◽  
Research Effort ◽  
Evidence Base ◽  
Pharmacological Therapy ◽  
Sufficient Evidence ◽  
Behavioural Treatment ◽  
Significant Research ◽  
Research Gap ◽  
Meta Analyses

Objective Dementia is one of the most common illnesses worldwide, and is one of the most important causes of disability in older people. Currently, dementia affects over 35 million people around the globe. It is expected that this number will increase to 65.7 million by 2030. Early detection, diagnosis and treatment to control the principal behaviour symptoms may help reduce these numbers and delay the progression to more advanced and dangerous stages of this disorder with resultant increase quality of life for those affected. The main goal of the present systematic literature review was to examine contemporary evidence relating to non-pharmacological therapy in the treatment of dementia. Methods To achieve the study goal, the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was used. Results This study identified the five most common behaviours in patients with dementia as aggression, wandering, agitation, apathy and sleep disturbances. Two non-pharmacological therapies were the most studied treatment: music therapy and aromatherapy. Ten other non-pharmacological therapies were also identified, but these lack a sufficient evidence-base. Conclusion Although all the therapies identified could be used as part of the treatment of behavioural symptoms, there is insufficient evidence relating to the indications, appropriate use and effectiveness of these therapies to apply in each behavioural treatment. Thus, the present study has demonstrated a significant research gap. What is known about the topic? Despite the widespread use of many different types of therapies, there is limited evidence regarding the efficacy of non-pharmaceutical therapies deployed in the management of behaviours of concern manifested by some people who suffer with dementia in all its forms. What does this paper add? This systematic review examines contemporary evidence from the literature to determine whether there is an evidence base available that would underpin the use of these therapies. This report on a PRISMA systematic review of the available literature demonstrates that only two therapies have some evidence to underpin the use of these non-pharmaceutical therapies and that a significant research gap is exists. What are the implications for practitioners? The implications for practitioners is that significant research effort is required to determine the efficacy of many of the therapies that are currently deployed, and thus many of the therapies used lack an evidence base at this time.

scholarly journals On Mixed Codes with Covering Radius $1$ and Minimum Distance $2$

10.37236/969 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Wolfgang Haas ◽  
Jörn Quistorff
Keyword(s):  
Lower Bounds ◽  
Minimum Distance ◽  
Covering Radius ◽  
Minimal Cardinality ◽  
Finite Sets ◽  
Open Problems ◽  
Latin Rectangle ◽  
Mixed Codes ◽  
Special Case

Let $R$, $S$ and $T$ be finite sets with $|R|=r$, $|S|=s$ and $|T|=t$. A code $C\subset R\times S\times T$ with covering radius $1$ and minimum distance $2$ is closely connected to a certain generalized partial Latin rectangle. We present various constructions of such codes and some lower bounds on their minimal cardinality $K(r,s,t;2)$. These bounds turn out to be best possible in many instances. Focussing on the special case $t=s$ we determine $K(r,s,s;2)$ when $r$ divides $s$, when $r=s-1$, when $s$ is large, relative to $r$, when $r$ is large, relative to $s$, as well as $K(3r,2r,2r;2)$. Some open problems are posed. Finally, a table with bounds on $K(r,s,s;2)$ is given.

scholarly journals On Reay's Relaxed Tverberg Conjecture and Generalizations of Conway's Thrackle Conjecture

10.37236/6516 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Megumi Asada ◽  
Ryan Chen ◽  
Florian Frick ◽  
Frederick Huang ◽  
Maxwell Polevy ◽  
...  
Keyword(s):  
Geometric Property ◽  
Convex Sets ◽  
Convex Hulls ◽  
Open Problems ◽  
Higher Dimensional ◽  
Special Cases ◽  
Minimum Number ◽  
Point Set ◽  
Colored Version ◽  
Special Case

Reay's relaxed Tverberg conjecture and Conway's thrackle conjecture are open problems about the geometry of pairwise intersections. Reay asked for the minimum number of points in Euclidean $d$-space that guarantees any such point set admits a partition into $r$ parts, any $k$ of whose convex hulls intersect. Here we give new and improved lower bounds for this number, which Reay conjectured to be independent of $k$. We prove a colored version of Reay's conjecture for $k$ sufficiently large, but nevertheless $k$ independent of dimension $d$. Pairwise intersecting convex hulls have severely restricted combinatorics. This is a higher-dimensional analogue of Conway's thrackle conjecture or its linear special case. We thus study convex-geometric and higher-dimensional analogues of the thrackle conjecture alongside Reay's problem and conjecture (and prove in two special cases) that the number of convex sets in the plane is bounded by the total number of vertices they involve whenever there exists a transversal set for their pairwise intersections. We thus isolate a geometric property that leads to bounds as in the thrackle conjecture. We also establish tight bounds for the number of facets of higher-dimensional analogues of linear thrackles and conjecture their continuous generalizations.

Uniqueness, definability and interpolation

1988 ◽  
Vol 53 (2) ◽  
pp. 554-570 ◽  
Author(s):  
Kosta Došen ◽  
Peter Schroeder-Heister
Keyword(s):  
Proof Theory ◽  
Interpolation Theorem ◽  
Order Logic ◽  
First Order Logic ◽  
General Notion ◽  
Structural Part ◽  
First Order ◽  
First Case ◽  
Additional Constant ◽  
Special Case

This paper is meant to be a comment on Beth's definability theorem. In it we shall make the following points.Implicit definability as mentioned in Beth's theorem for first-order logic is a special case of a more general notion of uniqueness. If α is a nonlogical constant, Tα a set of sentences, α* an additional constant of the same syntactical category as α and Tα, a copy of Tα with α* instead of α, then for implicit definability of α in Tα one has, in the case of predicate constants, to derive α(x1,…,xn) ↔ α*(x1,…,xn) from Tα ∪ Tα*, and similarly for constants of other syntactical categories. For uniqueness one considers sets of schemata Sα and derivability from instances of Sα ∪ Sα* in the language with both α and α*, thus allowing mixing of α and α* not only in logical axioms and rules, but also in nonlogical assumptions. In the first case, but not necessarily in the second one, explicit definability follows. It is crucial for Beth's theorem that mixing of α and α* is allowed only inside logic, not outside. This topic will be treated in §1.Let the structural part of logic be understood roughly in the sense of Gentzen-style proof theory, i.e. as comprising only those rules which do not specifically involve logical constants. If we restrict mixing of α and α* to the structural part of logic which we shall specify precisely, we obtain a different notion of implicit definability for which we can demonstrate a general definability theorem, where a is not confined to the syntactical categories of nonlogical expressions of first-order logic. This definability theorem is a consequence of an equally general interpolation theorem. This topic will be treated in §§2, 3, and 4.

Basic Geometric Dispersion Theory of Decision Making Under Risk: Asymmetric Risk Relativity, New Predictions of Empirical Behaviors, and Risk Triad

2021 ◽  
Author(s):  
Behnam Malakooti ◽  
Mohamed Komaki ◽  
Camelia Al-Najjar
Keyword(s):  
Risk Behaviors ◽  
Empirical Studies ◽  
Dispersion Theory ◽  
Dispersion Models ◽  
Decision Making Under Risk ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Out Of Sample ◽  
Mean Variance ◽  
Special Case

Many studies have spotlighted significant applications of expected utility theory (EUT), cumulative prospect theory (CPT), and mean-variance in assessing risks. We illustrate that these models and their extensions are unable to predict risk behaviors accurately in out-of-sample empirical studies. EUT uses a nonlinear value (utility) function of consequences but is linear in probabilities, which has been criticized as its primary weakness. Although mean-variance is nonlinear in probabilities, it is symmetric, contradicts first-order stochastic dominance, and uses the same standard deviation for both risk aversion and risk proneness. In this paper, we explore a special case of geometric dispersion theory (GDT) that is simultaneously nonlinear in both consequences and probabilities. It complies with first-order stochastic dominance and is asymmetric to represent the mixed risk-averse and risk-prone behaviors of the decision makers. GDT is a triad model that uses expected value, risk-averse dispersion, and risk-prone dispersion. GDT uses only two parameters, z and zX; these constants remain the same regardless of the scale of risk problem. We compare GDT to several other risk dispersion models that are based on EUT and/or mean-variance, and identify verified risk paradoxes that contradict EUT, CPT, and mean-variance but are easily explainable by GDT. We demonstrate that GDT predicts out-of-sample empirical risk behaviors far more accurately than EUT, CPT, mean-variance, and other risk dispersion models. We also discuss the underlying assumptions, meanings, and perspectives of GDT and how it reflects risk relativity and risk triad. This paper covers basic GDT, which is a special case of general GDT of Malakooti [Malakooti (2020) Geometric dispersion theory of decision making under risk: Generalizing EUT, RDEU, & CPT with out-of-sample empirical studies. Working paper, Case Western Reserve University, Cleveland.].

Acquisition of attributive adjectives and noun adjuncts by L3 learners of French and German: further evidence for the typological primacy model (TPM)

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Maryam Jamali ◽  
Ali Akbar Jabbari ◽  
Mohammad Hasan Razmi
Keyword(s):  
Task Performance ◽  
First Language ◽  
Facilitative Effect ◽  
Third Language ◽  
L3 Acquisition ◽  
Proficiency Level ◽  
Attributive Adjective ◽  
French Group ◽  
The Impact ◽  
Attributive Adjectives

Abstract This investigation explored the impact of prior acquired languages in the acquisition of third language (L3) at initial stages. The required data were gathered via two groups of L3 learners: 27 learners of L3 French and 26 learners of L3 German during a grammaticality judgement task (GJT) and an element rearrangement task (ERT) to test the placement of noun adjuncts and attributive adjectives. Both groups had acquired Persian as the first language and English as the second language. The participants were assigned to two L2 proficiency level groups (intermediate and advanced). The findings revealed that L3 German participants outperformed L3 French learners in the attributive adjective placement in both tasks as well as the noun adjunct in the GJT task. The L3 groups showed similar levels of performance in the ERT noun adjunct task. Additionally, the effect of L2 level of proficiency was not significant. The results also indicated that the typological similarity of L2 English to German rather than French rendered a facilitative effect on task performance in the L3 German group and a non-facilitative effect in the L3 French group. This study provides evidence for the Typological Primacy Model (TPM) of L3 acquisition suggesting that L3 learners are influenced by the typological similarities of the previous languages they have already acquired.

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