Miracle-dz/UniFAR-FTUs huggingface dataset:
Advances in Discrete and Computational Geometry

Geometric range searching and its relatives by P. K. Agarwal and J. Erickson Deformed products and maximal shadows of polytopes by N. Amenta and G. M. Ziegler Flag complexes, labelled rooted trees, and star shellings by L. J. Billera, C. S. Chan, and N. Liu Discrepancy bounds for geometric set systems with square incidence matrices by B. Chazelle Computational topology by T. K. Dey, H. Edelsbrunner, and S. Guha Recent progress on packing and covering by G. Fejes Toth Acoptic polyhedra by B. Grunbaum A proof of the strict monotone 4-step conjecture by F. Holt and V. Klee Interactions between real algebraic geometry and discrete and computational geometry by I. Itenberg and M. -F. Roy Open problems in the combinatorics of visibility and illumination by J. O'Rourke Halving lines and perfect cross-matchings by J. Pach and J. Solymosi Three-dimensional grid drawings of graphs by J. Pach, T. Thiele, and G. Toth On polygonal covers by M. Pocchiola and G. Vegter The universality theorems for oriented matroids and polytopes by J. Richter-Gebert Periodic and aperiodic tilings of $E^n$ by M. Senechal The early years of computational geometry-A personal memoir by M. I. Shamos Arrangements of surfaces in higher dimensions by M. Sharir Geometric discrepancy theory by J. Spencer Proof of Reay's conjecture on certain positive-dimensional intersections by H. Tverberg Progress in geometric transversal theory by R. Wenger Recent progress on polytopes by G. M. Ziegler Application challenges to computational geometry (CG impact task force report).
Sharpening the response of a symmetric nonrecursive filter by multiple use of the same filter

When processing data by filters we often find it necessary to improve the performance of the filter, either by increasing the out-of-band rejection (loss) or by decreasing the error in the passband, or both. A first approach is to process the data by repeated passes through the same filter. Each pass, while increasing the out-of-band loss, also increases the passband error, often to an undesirable level. It also increases the length (order) of the equivalent filter. How can we do a better job of filtering by suitably combining the results of several passes through the same filter? By "better" we mean both less passband error and greater out-of-band, or stopband, loss. This process is called filter sharpening. A simple, powerful method for doing this is described in detail, and its computational efficiency is compared to the best possible filter designs meeting the same specifications. The design method, based on the idea of the amplitude change function, is restricted to symmetric nonrecursive (finite impulse response) filters with piecewise constant pass and stopbands. Several illustrative examples are given.
Ruling Out Short Proofs of Unprovable Sentences is Hard

If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts about noncomputability into complexity theory. For instance, because proving string $x$ is Kolmogorov random ($x{\in}R$) is typically impossible, it is typically hard to prove"no length $t$ proof shows $x{\in}R$", or tautologies encoding this. Therefore, a proof system with one family of hard tautologies has these densely in an enumeration of families. The assumption also implies that a natural language is $\textbf{NP}$-intermediate: with $R$ redefined to have a sparse complement, the complement of the language $\{\langle x,1^t\rangle|$ no length $t$ proof exists of $x{\in}R\}$ is also sparse. Efficiently ruling out length $t$ proofs of $x{\in}R$ might violate the constraint on using the fact of $x{\in}R$'s unprovability. We conjecture: any computable predicate on $R$ that might be used in if-then statements (or case-based proofs) does no better than branching at random, because $R$ appears random by any effective test. This constraint could also inhibit the usefulness in circuits and propositional proofs of NOT gates and cancellation -- needed to encode if-then statements. If $R$ defeats if-then logic, exhaustive search is necessary.
On Unsteadiness in 2-D and 3-D Shock Wave Turbulent Boundary Layer Interactions

Shock-boundary layer interactions (SBLIs) are ubiquitous occurrences in supersonic and hypersonic vehicles and have the tendency to inhibit their structural and aerodynamic performance. For example, in the inlets and isolators of such vehicles, the shock wave generated by one surface interacts with the boundary layer on an adjacent one. They are also present on the exterior of the vehicles, e.g. at the fuselage/vertical stabilizer junctions. These interactions cause unsteady separation, resulting in reduced air in-take efficiency, or unstart in extreme cases; unsteady vortex shedding which yields undesirable broadband noise; and significant pressure fluctuations which compromise the structural integrity of the vehicle and which can lead to loss of control authority. Mitigating these issues is therefore an important part of optimizing aerodynamic and structural design of high speed vehicles. The first step in this respect is obtaining a better understanding of the interaction unsteadiness. Nominally 2-D interactions have been studied extensively and have identified low-frequency shock motions which lead to undesirable pressure loads. The particular frequencies associated with the motions have been characterized using time resolved experiments and computations, and shown to depend on the mean size of the separation. The physical processes responsible for these frequencies are however still under investigation and the physical relationship between the shock motions and pulsations of the separation bubble remains obscure. For flow fields where the shock is swept, a complex 3-D interaction is encountered whose unsteady features are even less well understood. The mean structure of these 3-D interactions has been obtained experimentally and using RANS simulations, and shown to be profoundly
New algebraic fast algorithms for N-body problems in two and three dimensions

This article presents two new algebraic algorithms to perform fast matrix-vector product for $N$-body problems in $d$ dimensions, namely nHODLR$d$D (nested algorithm) and s-nHODLR$d$D (semi-nested or partially nested algorithm). The nHODLR$d$D and s-nHODLR$d$D algorithms are the nested and semi-nested version of our previously proposed fast algorithm, the hierarchically off-diagonal low-rank matrix in $d$ dimensions (HODLR$d$D), respectively, where the admissible clusters are the certain far-field and the vertex-sharing clusters. We rely on algebraic low-rank approximation techniques (ACA and NCA) and develop both algorithms in a black-box (kernel-independent) fashion. The initialization time of the proposed hierarchical structures scales quasi-linearly. Using the nHODLR$d$D and s-nHODLR$d$D hierarchical structures, one can perform the multiplication of a dense matrix (arising out of $N$-body problems) with a vector that scales as $\mathcal{O}(pN)$ and $\mathcal{O}(pN \log(N))$, respectively, where $p$ grows at most poly logarithmically with $N$. The numerical results in $2$D and $3$D $(d=2,3)$ show that the proposed nHODLR$d$D algorithm is competitive to the algebraic Fast Multipole Method in $d$ dimensions with respect to the matrix-vector product time and space complexity. The C++ implementation with OpenMP parallelization of the proposed algorithms is available at \url{https://github.com/riteshkhan/nHODLRdD/}.
Interpretation of geophysical fields in complicated environments

Editors' Preface. Introduction. 1. Peculiarities of the Media Under Study and their Geophysical Investigations. 2. Common Aspects of Geophysical Fields in Question. 3. Informational Content and Structure of the Interpretation Process. 4. Development of the Initial Model of the Medium. 5. Indicator Space Generation. 6. Revealing and Localization of Targets. 7. Determination of the Anomalous Body Parameters. 8. Integrated Interpretation. 9. Revision of a Model of a Medium Representation and Evaluation of Interpretation Results. 10. Characteristic Features of the IMIGO Package. Conclusion. Appendix A: Elimination of Time Variations in the VLF Method and Near-Surface Thermal Prospecting. Appendix B: Description of the GSFC Program. References. Index.
Trend Analysis of Precipitation in Recent two Decades over Iran

Stationarity is an important assumption in most applications of hydrological time series modeling. It is thus necessary to test stationary before using those models. Time series are stationary when the statistical parameters of data such of average and variance will be independent of time. Most hydrological time series are nonstationary and it is necessary to identify components and factors of no stationary. One of the main factors of nonstationary in most time series is presence of trend. In this study trend analysis is done using measured annual precipitation in 140 synoptic stations over Iran in the period of 1990 to 2010. Seven synoptic stations in different climates selected and trend analysis has been done by Mann-Kendall and Spearman tests. Comparing MannKendall and Spearman tests showed that there were no significant differences between results of two methods. Trend analysis results by Mann-Kendall test showed that in Kabutarabad and Ardestan stations in Isfahan province any trend detected. In the Sistan Baluchestan, Khozestan, Kerman and Fras provinces at Zabol, Izeh and Bam stations significant downward trend observed at 1 and 5 percent levels. In other stations and provinces
Catheter Ablation of Persistent AF—Where are We Now?

Persistent atrial fibrillation (AF) is a diverse condition that includes various subtypes and underlying causes of arrhythmia. Progress made in catheter ablation technology in recent years has significantly enhanced the durability of ablation. Despite these advances however, the effectiveness of ablation in treating persistent AF is still relatively modest. Studies exploring the mechanisms behind persistent AF have identified substrate-driven focal and re-entrant sources within the atrial body as crucial in sustaining AF among individuals with persistent AF. Furthermore, the widespread adoption of atrial late gadolinium enhancement cardiac magnetic resonance (CMR) imaging and the ongoing refinement of invasive voltage mapping techniques have allowed for detailed assessment of fibrotic remodelling prior to or at the time of procedure. Translation into clinical practice, however, has yielded overall disappointing results. The clinical application of AF mapping in ablation procedures has not shown any substantial advantages beyond the use of pulmonary vein isolation (PVI) alone and adjunct ablation of fibrotic areas has yielded conflicting results in recent randomized trials. The emergence of pulsed field ablation represents a welcome development in the field and several studies have demonstrated an enhanced safety profile and increased procedural efficiency with this non-thermal energy modality. Pulsed field ablation also holds promise for safe and efficient substrate ablation beyond the pulmonary veins, but further trials are needed to assess its impact on longer term success rates. Continued advancements in our comprehension of AF mechanisms, alongside ongoing developments in catheter technology aimed at safe formation of transmural lesions, are essential for achieving better clinical outcomes for patients with persistent AF.
HGE: Embedding Temporal Knowledge Graphs in a Product Space of Heterogeneous Geometric Subspaces

Temporal knowledge graphs represent temporal facts (s,p,o,? ) relating a subject s and an object o via a relation label p at time ? , where ? could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.
Personalization of the Search Process in Tourism

The combination of travel and tourism represents the leading domain for applications in B2C e-commerce. Thus, it deserves highest attention. Since most people only have a very limited number of vacation days each year, they have learned to be more demanding about their trips. More and more they ask for better-personalized travel products instead of standard packages designed by tourist operators. Due to insufficient search engines and the lack of personalization, however, arranging a trip on current online travel portals is often not as easy as it should be. Even for rather straightforward scenarios, searching and booking a suitable travel package can be tedious and might often take longer than 1 hour. In order to provide good sales experiences and custom-tailored products similar to the ones competent human travel agents can offer, a personalized search approach for online travel portals has been overdue for some time. This thesis, therefore, presents a novel personalized search process delivering travel products exactly tailored to customers with respect to their situations and preferences. In a first step, a novel model for the search process in electronic commerce will be introduced. A deep personalization of the search will be provided by dividing the process into four stages, namely Preference Analysis & Modeling, Search Interface, Query Processing, and Presentation. The main part of this thesis, will then apply the new model to the tourism domain, i.e. each step of the search will be examined in the context of tourism. A situation model adequately adjusted to the tourism domain will then provide each stage of the search process with additional situational knowledge. Based on this, several essential components for a domain specific search in tourism will be introduced accordingly: a new preference constructor dealing with typical price-quality tradeoffs, a smart preference elicitation process supporting customers who have to find an optimal departure airport, the composition and evaluation of database queries supporting the interplay of individual and global preferences, and an appropriate adaptation of search interface and product presentation. Moreover, by using preference search technologies as underlying basis for the search itself, best alternatives can be delivered in case there is no perfect match. Several novel software components for a personalized search process in tourism have come into existence in the context of this thesis, e.g., the personalized prototype COSIMAT. The interplay of these components with existing preference components will be examined and evaluated by means of numerous use case scenarios at the end of this work. It will be demonstrated that by a proper combination of these components, custom-tailored travel products with respect to preferences and situations can be found and presented to the customer in an intuitive, fast and more comfortable manner than before.
Complex Document Information Processing : Towards Software and Test Collections

Complex document information processing (CDIP) is the analysis of combinations of handwritten notes, diagrams, and graphics in addition to printed and formatted text. Rapid analysis of collections of complex documents is increasingly critical to intelligence appraisals of hostile forces and other entities of interest. Such collections may be seized by military or law enforcement (recently in Iraq, Afghanistan, and elsewhere), or turned over by cooperating parties (e.g. defectors). This material must be scanned or otherwise input, understood, and exploited all in a short period of time if it is to be of maximum value. Such collections may contain many types of complex documents and data, and ideally should be interpreted in the context of previously obtained collections and knowledge. Unfortunately, most current tools are specialized to one kind of data (text content or style, handwriting, graphics, database records, etc.) and sometimes only one genre of document. Extracting intelligence from such collections therefore relies heavily on manual partitioning of data, coordination of analysis tools, and collation of results. Besides being slow, expensive, and demanding on the time of trained analysts, the current approach has two fundamental problems. First, the speed and accuracy of analyzing one data type can often be improved if partial analyses from other data types were available, but a collection of standalone tools does not support this. Second, manual collation, cross-checking, and consistency checking is slow and error-prone when dealing with large numbers of documents, further reducing the value of obtained information. The operational problem, therefore, is the dearth of unified tools for CDIP in both commercial and research spheres. That in itself, however, is symptomatic of a second problem: the lack of standard test collections for CDIP research. Test collections of documents (and manual judgments/annotations) in text retrieval and categorization, handwriting recognition, and data mining have sparked intense research and commercial development. Conversely, CDIP research and development is stifled by the lack of a test collection of complex documents. Creating a CDIP test collection is thus an essential component of any serious CDIP effort. II. BUILDING A CDIP SYSTEM
Higher moments of the error term in the divisor problem

AbstractIt is proved that, if k ≥ 2 is a fixed integer and 1 ≪ H ≤ (1/2)X, then $$ \int_{X - H}^{X + H} {\Delta _k^4 \left( x \right) } dx \ll _\varepsilon X^\varepsilon \left( {HX^{{{\left( {2k - 2} \right)} \mathord{\left/ {\vphantom {{\left( {2k - 2} \right)} k}} \right. \kern-\nulldelimiterspace} k}} + H^{{{\left( {2k - 3} \right)} \mathord{\left/ {\vphantom {{\left( {2k - 3} \right)} {\left( {2k + 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2k + 1} \right)}}} X^{{{\left( {8k - 8} \right)} \mathord{\left/ {\vphantom {{\left( {8k - 8} \right)} {\left( {2k + 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {2k + 1} \right)}}} } \right), $$ where Δk(x) is the error term in the general Dirichlet divisor problem. The proof uses a Voronoï-type formula for Δk(x), and the bound of Robert-Sargos for the number of integers when the difference of four kth roots is small. The size of the error term in the asymptotic formula for the mth moment of Δ2(x) is also investigated.
Partial Subliner Time Approximation and Inapproximation for Maximum Coverage

We develop a randomized approximation algorithm for the classical maximum coverage problem, which given a list of sets $A_1,A_2,\cdots, A_n$ and integer parameter $k$, select $k$ sets $A_{i_1}, A_{i_2},\cdots, A_{i_k}$ for maximum union $A_{i_1}\cup A_{i_2}\cup\cdots\cup A_{i_k}$. In our algorithm, each input set $A_i$ is a black box that can provide its size $|A_i|$, generate a random element of $A_i$, and answer the membership query $(x\in A_i? )$ in $O(1)$ time. Our algorithm gives $(1-{1\over e})$-approximation for maximum coverage problem in $O(p(n))$ time, which is independent of the sizes of the input sets. No existing $O(p(n)m^{1-\epsilon})$ time $(1-{1\over e})$-approximation algorithm for the maximum coverage has been found for any function $p(n)$ that only depends on the number of sets, where $m=\max(|A_1|,\cdots,| A_n|)$ (the largest size of input sets). The notion of partial sublinear time algorithm is introduced. For a computational problem with input size controlled by two parameters $n$ and $m$, a partial sublinear time algorithm for it runs in a $O(p(n)m^{1-\epsilon})$ time or $O(q(m)n^{1-\epsilon})$ time. The maximum coverage has a partial sublinear time $O(p(n))$ constant factor approximation. On the other hand, we show that the maximum coverage problem has no partial sublinear $O(q(m)n^{1-\epsilon})$ time constant factor approximation algorithm. It separates the partial sublinear time computation from the conventional sublinear time computation by disproving the existence of sublinear time approximation algorithm for the maximum coverage problem.
[Results of photorefractive keratectomy in myopia with flying spot excimer laser with high speed and small beam diameter].

PURPOSE To examine the result of photorefractive keratectomy (PRK) with the next generation of flying spot excimer laser for the treatment of myopic refractive errors. PATIENTS AND METHODS During the study 164 eyes of 98 patients were assessed. The average age was 29.4 +/- 4.62 years. The myopic eyes were divided into 3 groups: in Group 1. (n = 115 eyes) the eyes between -1.0 D and -6.0 D were evaluated, in this group the preoperative average refraction was -3.43 +/- 1.2 D (SE = spherical equivalent); in Group 2. (n = 31 eyes) the eyes between -6.1 D and -9.0 D were evaluated; the preoperative average refraction was -7.26 +/- 2.4 D (SE). In Group 3. (n = 18 eyes) eyes above -9.0 D were examined; in Group 3. the average preoperative refraction was -10.22 +/- 3.4 D (SE) Follow-up is 6 months. PRK treatments were carried out with the Zeiss Meditec MEL 80 G-Scan flying spot excimer laser, which was operated with a 0.7 mm beam diameter and 250 Hz frequency. RESULTS In Group 1. The preoperative correction decreased to -0.14 D (SE); in 71% of the treated eyes uncorrected visual acuity (UCVA) was 1.0; in 24% of the eyes UCVA improved to 1.2. Best corrected visual acuity (BCVA) was unchanged in 65% of the eyes; while in 34 improved (in 24% it improved by more than 2) Snellen lines. In Group 2. the preoperative correction decreased to -0.13 +/- 0.01 D (SE); 67% had 1.0 and 8% had a 1.2 UCVA. BCVA was unchanged in 92% in Group 2. ; in 8% BCVA increased by 1 or 2 Snellen lines. In Group 3. , the preoperative correction decreased to -0.44 +/- 0.2 D (SE); 96% of the eyes had a 0.8 UCVA; BCVA did not change in 75% of the eyes, 25% of the eyes gained 1 Snellen line. CONCLUSIONS Myopic PRK treatments with the 3rd generation of excimer laser were effective and safe. Regarding BCVA, best results were obtained in the low and medium myopia groups.
Cigarettes, Smokeless Tobacco, and Poly-Tobacco Among Workers in Three Dusty Industries

Background: Tobacco use remains high among blue-collar workers, the health consequences of which may be compounded by occupational dust exposure. Detailed data on tobacco use among workers in dusty industries are lacking. Methods: The 2006 to 2012 National Survey on Drug Use and Health was used to compare current tobacco use prevalence [including cigarettes, smokeless tobacco (SLT), and both (dual use)] among male workers in three dusty industries to all other employed men using bivariate and multivariate analysis. Results: Smoking rates were high among extraction (39.9%) and construction (38.5%) workers. Increased odds of SLT (odds ratio = 3.3) and dual use (odds ratio = 2.6) were observed among dusty-industry workers compared with other employed men. The prevalence of any tobacco use was unexpectedly high among extraction workers (60.4%). Conclusions: Disparities in tobacco use behaviors by industry may point to opportunities for targeted workplace tobacco cessation programs.