Weighted model integration (WMI) is a recent formalism generalizing weighted model counting (WMC) to run probabilistic inference over hybrid domains, characterized by both discrete and continuous ...variables and relationships between them. WMI is computationally very demanding as it requires to explicitly enumerate all possible truth assignments to be integrated over. Component caching strategies which proved extremely effective for WMC are difficult to apply in this formalism because of the tight coupling induced by the arithmetic constraints. In this paper we present a novel formulation of WMI, which allows to exploit the power of SMT-based predicate abstraction techniques in designing efficient inference procedures. A novel algorithm combines a strong reduction in the number of models to be integrated over with their efficient enumeration. Experimental results on synthetic and real-world data show drastic computational improvements over the original WMI formulation as well as existing alternatives for hybrid inference.
Let α,β∈0,1)=R/Z such that at least one of them is irrational. It is known that the random αβ-orbits of the Bernoulli mixture of rotations of α and β by choosing them with equal probability 12 are ...uniformly distributed modulo 1 with probability one. Chen et al. (2021) 2 showed that the exceptional set in the probability space has full Hausdorff dimension. In this note, we prove that certain sets related to random αβ-orbits which are not dense in R/Z have Hausdorff dimension 1. Our result can be viewed as an improvement of the dimension result obtained by Chen, Wang and Wen.
Performance of modulo-(2n+1) arithmetic is enhanced via D1 encoding versus normal (n+1)-bit encoding of residues in 0, 2n. Faster modulo-(2n+1) operations promote the latency balance with the ...commonly companion modulus (2n−1) and 2n in residue number system arithmetic. However, the cases of zero inputs/output of D1 arithmetic circuits entail especial handling, with some overhead. Despite many studies over modulo-(2n+1) D1 adders, where the least achieved latency is (3+ 2⌈log n⌉)ΔG, there has been few works on the D1 subtraction. However, the lowest reported performance for the latter is (7+ 2⌈log n⌉)ΔG. In this paper, we revisit the fastest previous (D1 adder, propose an as fast D1 subtractor, and a (5+ 2⌈log n⌉)ΔG unified D1 adder/subtractor, with minimal unification overhead (i.e., one XOR/bit), all with full zero handling. Compared to the best of previous relevant works, we demonstrate 18–34% less delay and 5–18% less energy for the ensemble three modulus of the set {2n−1, 2n,2n+1}.
We show that, for each natural number k>1, every graph (possibly with multiple edges but with no loops) of edge-connectivity at least 2k2+k has an orientation with any prescribed outdegrees modulo k ...provided the prescribed outdegrees satisfy the obvious necessary conditions. For k=3 the edge-connectivity 8 suffices. This implies the weak 3-flow conjecture proposed in 1988 by Jaeger (a natural weakening of Tutteʼs 3-flow conjecture which is still open) and also a weakened version of the more general circular flow conjecture proposed by Jaeger in 1982. It also implies the tree-decomposition conjecture proposed in 2006 by Bárat and Thomassen when restricted to stars. Finally, it is the currently strongest partial result on the (2+ϵ)-flow conjecture by Goddyn and Seymour.
Let
p
be a positive real-valued continuous function on
R
+
such that the function
P
(
x
)
=
∫
0
x
p
(
t
)
d
t
,
x
>
0
,
is regularly varying with a positive index in the Karamata sense. For a real- ...or complex-valued continuous function
f
on
R
+
, we define
s
(
x
)
=
∫
0
x
f
(
y
)
d
y
and
σ
p
(
x
)
=
1
P
(
x
)
∫
0
x
s
(
y
)
p
(
y
)
d
y
.
It is known that if the finite limit
lim
x
→
∞
s
(
x
)
=
L
exists, then so does
lim
x
→
∞
σ
p
(
x
)
=
L
. In this paper, we introduce some Tauberian conditions in terms of the weighted classical control modulo and the weighted general control modulo of order one under which the converse implication and its extensions hold. Our results generalize some classical type Tauberian theorems existing in the literature.
Missing Values Management is one of the challenges faced by Data Analysts. Therefore, the creation of effective data models will be the right decision for missing data imputation. However, learning, ...training, and Data Analysis must be implemented through machine learning algorithms. Missing Data is a problem with no feedback or variables. This problem (missing data) can result in serious Data Analysis, which may eventually lead to erroneous conclusions. This research paper first studies how missing data can affect Machine Learning Algorithms, and decision-making based on the Data Analysis’s output. Secondly, it proposes Modulo 9 as a novel method for handling missing data problems. The proposed novel method is assessed with wide-ranging experiments compared with robust Machine Learning techniques such as Support Vector Machine (SVM) Algorithm, Linear Regression (LR), K-Nearest Neighbors (KNN), Naïve Bayes (NB), Support Vector Classifier (SVC), Linear Support Vector Classifier (LSVC), Random Forest Classifier (RFC), Decision Tree Regressor (DTR), Deletion Method, Multi-Layer Perceptron (MLP), and the Mean Value. The results show that the novel method outperforms the eleven (11) existing methods.
•A novel method named modulo 9 as a new method of handling missing data.•Demonstrating how missing data can affect machine learning algorithms and the decisions making.•Application of robust machine learning techniques, deletion method and the average.•Performances of the methods on the dataset containing missing data.
This study investigates the properties of a composite material obtained by mixing Fe78Si9B13 metallic powders (at %) with graphene nanoplates (GNP) in an epoxy matrix. Four composite types were ...created with GNP weight proportions of 0%, 0.5%, 1.0%, and 1.5%. The composites were embedded in transparent epoxy with weight proportions of 10%, 15%, and 20%, and then filled into 7 x 20 mm cylindrical probes. Twelve samples were prepared, and another 12 samples were subjected to a longitudinal magnetic field of 1 kG. All samples were tested with a Universal Testing Machine (Model WDW 10E) up to a maximum force of 20 kN. The experiment recorded deformation (ΔH) vs. charge force. Most samples showed a maximum compression resistance of 390 MPa, except for a few that did not exceed 100 MPa. The magnetically oriented samples showed a greater elastic limit in the range of 200 to 270 MPa. Optical microscopy was used to observe the ordering of the particles after the application of the magnetic field. Scanning electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray diffraction were used to characterize the structure of the composite components. A vibrating sample magnetometer (VSM) was used to characterize the magnetic behavior of the metallic powders in the composite.
Periodic elements and lifting connections Khurana, Dinesh; Nielsen, Pace P.
Journal of pure and applied algebra,
November 2023, 2023-11-00, Volume:
227, Issue:
11
Journal Article
Peer reviewed
It is well-known that idempotents lift modulo any nil one-sided ideal. While this is not true for periodic elements, it does hold true in many special cases. We investigate the connections between ...these special cases, as well as limitations. We also answer three questions from the literature. For example, we construct a nilpotent ideal where torsion-units lift, but periodic elements do not lift, modulo that ideal.
We consider codimension 1 area-minimizing m-dimensional currents T mod an even integer p=2Q in a C2 Riemannian submanifold Σ of Euclidean space. We prove a suitable excess-decay estimate towards the ...unique tangent cone at every point q∈spt(T)∖sptp(∂T) where at least one such tangent cone is Q copies of a single plane. While an analogous decay statement was proved in Minter and Wickramasekera (2024) as a corollary of a more general theory for stable varifolds, in our statement we strive for the optimal dependence of the estimates upon the second fundamental form of Σ. This improvement is in fact crucial in De Lellis et al., (2022) to prove that the singular set of T can be decomposed into a C1,α(m−1)-dimensional submanifold and an additional closed remaining set of Hausdorff dimension at most m−2.
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