Author

# R G Ascoli

Bio: R G Ascoli is an academic researcher. The author has contributed to research in topics: Mathematics & Similarity (geometry). The author has an hindex of 1, co-authored 1 publications receiving 25 citations.

##### Papers

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TL;DR: In this paper, the authors investigated the characteristics of the pumiceous sand, including its standard penetration resistance and its cyclic loading characteristics, and found that the sand is somewhat lighter in weight than sand deposits which have liquefied in other earthquakes.

Abstract: One of the effects of the February 4, 1976, Guatemala earthquake was the extensive liquefaction which occurred at the settlement of La Playa on the northeast shore of Lake Amatitlan. Ground accelerations in the area resulting from the magnitude 7.5 earthquake are estimated to be of the order of 0.12 g to 0.15 g. The characteristics of the sand are investigated, including its standard penetration resistance and its cyclic loading characteristics. Despite the fact that the sand is somewhat lighter in weight than sand deposits which have liquefied in other earthquakes, its liquefaction characteristics are apparently influenced by the same factors as other sand deposits; its overall behavior is consistent with that exhibited by other sands. The high degree of liquefaction at the La Playa site was probably due in large measure to the lightweight nature of the pumiceous sands.

25 citations

03 Oct 2022

TL;DR: For the generalized dihedral group D = Z 2 (cid:110) G, the authors showed that there are more MSTD sets than MDTS sets when 6 ≤ m ≤ c j √ n for c j = 1 . 3229 / √ 111 + 5 j , where j is the number of elements in G with order at most 2.

Abstract: . Given a group G , we say that a set A ⊆ G has more sums than diﬀerences (MSTD) if | A + A | > | A − A | , has more diﬀerences than sums (MDTS) if | A + A | < | A − A | , or is sum-diﬀerence balanced if | A + A | = | A − A | . A problem of recent interest has been to understand the frequencies of these type of subsets. The seventh author and Vissuet studied the problem for arbitrary ﬁnite groups G and proved that almost all subsets A ⊆ G are sum-diﬀerence balanced as | G | → ∞ . For the dihedral group D 2 n , they conjectured that of the remaining sets, most are MSTD, i.e., there are more MSTD sets than MDTS sets. Some progress on this conjecture was made by Haviland et al. in 2020, when they introduced the idea of partitioning the subsets by size: if, for each m , there are more MSTD subsets of D 2 n of size m than MDTS subsets of size m , then the conjecture follows. We extend the conjecture to generalized dihedral groups D = Z 2 (cid:110) G , where G is an abelian group of size n and the nonidentity element of Z 2 acts by inversion. We make further progress on the conjecture by considering subsets with a ﬁxed number of rotations and reﬂections. By bounding the expected number of overlapping sums, we show that the collection S D,m of subsets of the generalized dihedral group D of size m has more MSTD sets than MDTS sets when 6 ≤ m ≤ c j √ n for c j = 1 . 3229 / √ 111 + 5 j , where j is the number of elements in G with order at most 2. We also analyze the expectation for | A + A | and | A − A | for A ⊆ D 2 n , proving an explicit formula for | A − A | when n is prime.

06 Oct 2022

TL;DR: In particular, the authors showed that a hypothesis class with finite VC-dimension is PAC-learnable under the assumption that the VC dimension of the hypothesis class is as large as possible.

Abstract: Given a domain $X$ and a collection $\mathcal{H}$ of functions $h:X\to \{0,1\}$, the Vapnik-Chervonenkis (VC) dimension of $\mathcal{H}$ measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions $\mathcal{H}_t^{'2}(E): \mathbb{F}_q^2\to \{0,1\}$, corresponding to indicator functions of circles centered at points in a subset $E\subseteq \mathbb{F}_q^2$. They showed that when $|E|$ is large enough, the VC-dimension of $\mathcal{H}_t^{'2}(E)$ is the same as in the case that $E = \mathbb F_q^2$. We study a related hypothesis class, $\mathcal{H}_t^d(E)$, corresponding to intersections of spheres in $\mathbb{F}_q^d$, and ask how large $E\subseteq \mathbb{F}_q^d$ needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever $|E|\geq C_dq^{d-1/(d-1)}$ for $d\geq 3$, the VC-dimension of $\mathcal{H}_t^d(E)$ is as large as possible. We get a slightly stronger result if $d=3$: this result holds as long as $|E|\geq C_3 q^{7/3}$. Furthermore, when $d=2$ the result holds when $|E|\geq C_2 q^{7/4}$.

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TL;DR: In this paper , Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolf provide bounds on the minimum number of distinct angles in general position in three dimensions.

Abstract: In 1946, Erd\H{o}s posed the distinct distance problem, which seeks to find
the minimum number of distinct distances between pairs of points selected from
any configuration of $n$ points in the plane. The problem has since been
explored along with many variants, including ones that extend it into higher
dimensions. Less studied but no less intriguing is Erd\H{o}s' distinct angle
problem, which seeks to find point configurations in the plane that minimize
the number of distinct angles. In their recent paper "Distinct Angles in
General Position," Fleischmann, Konyagin, Miller, Palsson, Pesikoff, and Wolf
use a logarithmic spiral to establish an upper bound of $O(n^2)$ on the minimum
number of distinct angles in the plane in general position, which prohibits
three points on any line or four on any circle.
We consider the question of distinct angles in three dimensions and provide
bounds on the minimum number of distinct angles in general position in this
setting. We focus on pinned variants of the question, and we examine explicit
constructions of point configurations in $\mathbb{R}^3$ which use
self-similarity to minimize the number of distinct angles. Furthermore, we
study a variant of the distinct angles question regarding distinct angle chains
and provide bounds on the minimum number of distinct chains in $\mathbb{R}^2$
and $\mathbb{R}^3$.

19 Jul 2023

TL;DR: In this article , the authors generalize Sun's result to arbitrary dimension and improve the exponent in the case $d=3, where the VC-dimension of the vector space is 3.

Abstract: Let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field with $q$ elements. For a subset $E\subseteq \mathbb{F}_q^d$ and a fixed nonzero $t\in \mathbb{F}_q$, let $\mathcal{H}_t(E)=\{h_y: y\in E\}$, where $h_y$ is the indicator function of the set $\{x\in E: x\cdot y=t\}$. Two of the authors, with Maxwell Sun, showed in the case $d=3$ that if $|E|\geq Cq^{\frac{11}{4}}$ and $q$ is sufficiently large, then the VC-dimension of $\mathcal{H}_t(E)$ is 3. In this paper, we generalize the result to arbitrary dimension and improve the exponent in the case $d=3$.

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TL;DR: In this article, a simplified procedure for evaluating the liquefaction potential of sand deposits using data obtained from standard penetration tests is reviewed, and the results of this study are then extended to other magnitude earthquakes using a combination of laboratory and field data.

Abstract: The evolution of a simplified procedure for evaluating the liquefaction potential of sand deposits using data obtained from standard penetration tests is reviewed. Field data for sites which are known to have liquefied or not liquefied during earthquakes in the United States, Japan, China, Guatemala, Argentina, and other countries are presented to establish a criterion for evaluating the liquefaction potential of sands in Magnitude 7‐1/2 earthquakes. The results of this study are then extended to other magnitude earthquakes using a combination of laboratory and field data. Available information on the liquefaction resistance of silty sands is also reviewed and a simple procedure for considering the influence of silt content is proposed. A method is presented for using the field data to evaluate the possible magnitude of pore water pressure generation in sands and silty sands which remain stable during earthquake shaking. Finally, the applicability of other in situ field tests, such as the static cone pene...

813 citations

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TL;DR: In this paper, the authors present new correlations for assessment of the likelihood of initiation (or triggering) of soil liquefaction, which eliminate several sources of bias intrinsic to previous, similar correlations, and provide greatly reduced overall uncertainty and variance.

Abstract: This paper presents new correlations for assessment of the likelihood of initiation (or “triggering”) of soil liquefaction. These new correlations eliminate several sources of bias intrinsic to previous, similar correlations, and provide greatly reduced overall uncertainty and variance. Key elements in the development of these new correlations are (1) accumulation of a significantly expanded database of field performance case histories; (2) use of improved knowledge and understanding of factors affecting interpretation of standard penetration test data; (3) incorporation of improved understanding of factors affecting site-specific earthquake ground motions (including directivity effects, site-specific response, etc.); (4) use of improved methods for assessment of in situ cyclic shear stress ratio; (5) screening of field data case histories on a quality/uncertainty basis; and (6) use of high-order probabilistic tools (Bayesian updating). The resulting relationships not only provide greatly reduced uncertai...

554 citations

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TL;DR: In this article, a genetic classification of soft-sediment deformation processes and structures is presented, which are combined to produce a genetic classifier of softsediment structures and deformation mechanisms.

Abstract: Summary Deformation in unconsolidated sands requires the action of a deformation mechanism to reduce sediment strength and a driving force to induce deformation. Deformation mechanisms include liquefaction and fluidization and are reflected in the style of deformation and grain orientation fabrics. They are initiated by a trigger, including groundwater movements, wave action and seismic shaking. Driving forces include gravitational body force, unevenly distributed loads, unstable density gradients and shear forces, and are reflected in the geometry of deformation. These components are combined to produce a genetic classification of soft-sediment deformation processes and structures.

332 citations

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TL;DR: In this article, a critical review of field performance of sandy soil deposits during past earthquakes was conducted with special emphasis being placed on Standard Penetration Test N-values and fines content.

331 citations

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TL;DR: The main types of seismites are reviewed following the proposed classification and are illustrated by their own case studies as mentioned in this paper, which depends on the sedimentologic, hydrodynamic and diagenetic characters of the deposits subject to seismic shocks.

291 citations