Parole and Probation in Alaska, 2002–2016

Underlying data is available in both Excel and PDF format. (Download below.)This fact sheet presents data on the characteristics of offenders who came under the supervision of the Alaska Department of Corrections, Division of Probation and Parole (DOC-PP) between 2002 and 2016. Probation and parole offender data are from the Alaska Department of Corrections’ annual Offender Profile publication. Overall trends saw numbers of probationers and parolees increasing from 2002 to 2012, then decreasing through 2016. The majority of probationers and parolees are between 20 and 34 years old. The trend for both males and females followed the overall trend, increasing from 2002 to 2012 then decreasing. On average, from 2002 to 2016, Alaska Natives were 26.7% of the probation and parole population, Asian & or Pacific Islander 4.1%, Black 8.7%, and White 56.1%.Overall / Age / Gender / Ethnicity / Summary / Note

Motor Vehicle Theft Arrests Reported in Alaska, 1985–2015

Data is available in both Excel and PDF format. (Download below.)This fact sheet presents data on motor vehicle theft arrests reported in Alaska from 1985 to 2016 as reported in the Alaska Department of Public Safety publication Crime in Alaska. Overall, the motor vehicle arrest rate consistently declined between 1990 and 2014 when it reached the lowest level in the 1985–2016 period. The motor vehicle arrest rate rebounded in 2015 and 2016. Increases in Alaska motor vehicle arrest rates in 2015 and 2016 were particularly pronounced among adults and males, while motor vehicle arrest rates for juveniles and females remained minimal in comparison. On average, adults accounted for 62.6 percent and juveniles for 37.4 percent of all arrests for motor vehicle thefts reported in Alaska from 1985 to 2016. Males accounted for 81.8 percent of all motor vehicle theft arrests, females 18.2 percent.Motor vehicle theft arrests / Oveally motor vehicle theft arrest rates / Arrest rates by age / Arrest rates by gender / Summary / Note

Convergence Rate of Riemannian Hamiltonian Monte Carlo and Faster Polytope Volume Computation

We give the first rigorous proof of the convergence of Riemannian Hamiltonian Monte Carlo, a general (and practical) method for sampling Gibbs distributions. Our analysis shows that the rate of convergence is bounded in terms of natural smoothness parameters of an associated Riemannian manifold. We then apply the method with the manifold defined by the log barrier function to the problems of (1) uniformly sampling a polytope and (2) computing its volume, the latter by extending Gaussian cooling to the manifold setting. In both cases, the total number of steps needed is O^{*}(mn^{\frac{2}{3}}), improving the state of the art. A key ingredient of our analysis is a proof of an analog of the KLS conjecture for Gibbs distributions over manifolds

Value of Stolen Property Reported in Alaska, 1985–2016

Data is available in both Excel and PDF format. (Download below.)This fact sheet presents data on the value of stolen property reported in Alaska from 1985 to 2016 as reported in the Department of Public Safety publication Crime in Alaska. Overall, the 31-year trend reveals that the total value of stolen property in Alaska was relatively static with a trough beginning in 2008 and rising in 2014. The increase in stolen property value from 2014 to 2016 was mainly due to increases in the aggregate values of stolen motor vehicles and miscellaneous items. After adjusting for inflation, the highest total value of stolen property was recorded in 1990 at $61,651,724. The lowest total value of stolen property recorded was in 2011 at$22,189,499. Of the different property types, motor vehicles represented the largest value and share of stolen property. On average, motor vehicles were 53.7% ($24,246,790 per year) of the total value of stolen property.Stolen property / Total value of stolen property / Currency, notes, etc. / Jewelry and precious metals / Clothing and furs / Locally stolen motor vehicles / Office equipment / TV, radios, cameras, etc. / Firearms / Household goods / Miscellaneous Summary / Note

Effect of Alaska Fiscal Options On Children and Families

Alaska’s state government faces an unprecedented challenge, with the need to close an estimated $3 billion gap between projected revenues and expenditures in fiscal year 2017. Total unrestricted state General Fund revenue in fiscal year 2016 (the 12 months ending June 30, 2016) was$1.3 billion, or about $1,800 per resident. That was barely more than the state dispenses annually to Alaska school districts, to support public education (Alaska Office of Management and Budget, Enacted Fiscal Summary). Despite low oil prices and declining production, petroleum revenues still accounted for 72 percent of these funds (Alaska Revenue Sources Book, Fall 2016, Alaska Department of Revenue, Tax Division). Alaska is the only state that does not have either state income or sales taxes. It is clear that Alaskans will soon have to accept some form of broad-based revenue measure to enable continued funding of basic public services. A 2016 analysis by ISER researchers discussed the potential effects on Alaska’s economy and households of various options to reduce expenditures and increase revenues.1 That study examined how the effects of revenue measures varied for Alaska households with different levels of income. These same revenue measures and expenditure cuts are also likely to have a much bigger effect on some households than others, depending on the presence and number of children in the family. This study extends the previous analysis by specifically examining how different options would be likely to affect families and children. Many large expenditures in the state budget can easily be identified as specifically benefiting children. These include state-funded programs such as the Alaska Public School Foundation program and the Division of Juvenile Justice and Office of Children’s Services, for example, as well as joint federal-state programs such as Medicaid and Denali Kidcare. Less obvious are the effects on children of potential measures to fund these and other state expenditures. This study focuses on describing and quantifying the effects of alternative state revenue options on Alaska families and children. In addition to considering how the revenue measures might affect families with children compared to households without children, we also consider how the burden of each measure might differ for rural and urban families.National Science Foundation Alaska Children's Trust UA Strategic Investment FUnd

Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices

We consider $N\times N$ Hermitian random matrices with i.i.d. entries. The matrix is normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. We study the connection between eigenvalue statistics on microscopic energy scales $\eta\ll1$ and (de)localization properties of the eigenvectors. Under suitable assumptions on the distribution of the single matrix elements, we first give an upper bound on the density of states on short energy scales of order $\eta \sim\log N/N$. We then prove that the density of states concentrates around the Wigner semicircle law on energy scales $\eta\gg N^{-2/3}$. We show that most eigenvectors are fully delocalized in the sense that their $\ell^p$-norms are comparable with $N^{{1}/{p}-{1}/{2}}$ for $p\ge2$, and we obtain the weaker bound $N^{{2}/{3}({1}/{p}-{1}/{2})}$ for all eigenvectors whose eigenvalues are separated away from the spectral edges. We also prove that, with a probability very close to one, no eigenvector can be localized. Finally, we give an optimal bound on the second moment of the Green function.Comment: Published in at http://dx.doi.org/10.1214/08-AOP421 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Strongly Refuting Random CSPs Below the Spectral Threshold

Random constraint satisfaction problems (CSPs) are known to exhibit threshold phenomena: given a uniformly random instance of a CSP with $n$ variables and $m$ clauses, there is a value of $m = \Omega(n)$ beyond which the CSP will be unsatisfiable with high probability. Strong refutation is the problem of certifying that no variable assignment satisfies more than a constant fraction of clauses; this is the natural algorithmic problem in the unsatisfiable regime (when $m/n = \omega(1)$). Intuitively, strong refutation should become easier as the clause density $m/n$ grows, because the contradictions introduced by the random clauses become more locally apparent. For CSPs such as $k$-SAT and $k$-XOR, there is a long-standing gap between the clause density at which efficient strong refutation algorithms are known, $m/n \ge \widetilde O(n^{k/2-1})$, and the clause density at which instances become unsatisfiable with high probability, $m/n = \omega (1)$. In this paper, we give spectral and sum-of-squares algorithms for strongly refuting random $k$-XOR instances with clause density $m/n \ge \widetilde O(n^{(k/2-1)(1-\delta)})$ in time $\exp(\widetilde O(n^{\delta}))$ or in $\widetilde O(n^{\delta})$ rounds of the sum-of-squares hierarchy, for any $\delta \in [0,1)$ and any integer $k \ge 3$. Our algorithms provide a smooth transition between the clause density at which polynomial-time algorithms are known at $\delta = 0$, and brute-force refutation at the satisfiability threshold when $\delta = 1$. We also leverage our $k$-XOR results to obtain strong refutation algorithms for SAT (or any other Boolean CSP) at similar clause densities. Our algorithms match the known sum-of-squares lower bounds due to Grigoriev and Schonebeck, up to logarithmic factors. Additionally, we extend our techniques to give new results for certifying upper bounds on the injective tensor norm of random tensors

Solution space heterogeneity of the random K-satisfiability problem: Theory and simulations

The random K-satisfiability (K-SAT) problem is an important problem for studying typical-case complexity of NP-complete combinatorial satisfaction; it is also a representative model of finite-connectivity spin-glasses. In this paper we review our recent efforts on the solution space fine structures of the random K-SAT problem. A heterogeneity transition is predicted to occur in the solution space as the constraint density alpha reaches a critical value alpha_cm. This transition marks the emergency of exponentially many solution communities in the solution space. After the heterogeneity transition the solution space is still ergodic until alpha reaches a larger threshold value alpha_d, at which the solution communities disconnect from each other to become different solution clusters (ergodicity-breaking). The existence of solution communities in the solution space is confirmed by numerical simulations of solution space random walking, and the effect of solution space heterogeneity on a stochastic local search algorithm SEQSAT, which performs a random walk of single-spin flips, is investigated. The relevance of this work to glassy dynamics studies is briefly mentioned.Comment: 11 pages, 4 figures. Final version as will appear in Journal of Physics: Conference Series (Proceedings of the International Workshop on Statistical-Mechanical Informatics, March 7-10, 2010, Kyoto, Japan

Uniqueness, spatial mixing, and approximation for ferromagnetic 2-spin systems

For anti-ferromagnetic 2-spin systems, a beautiful connection has been established, namely that the following three notions align perfectly: The uniqueness of Gibbs measures in infinite regular trees, the decay of correlations (also known as spatial mixing), and the approximability of the partition function. The uniqueness condition implies spatial mixing, and an FPTAS for the partition function exists based on spatial mixing. On the other hand, non-uniqueness implies some long range correlation, based on which NP-hardness reductions are built. These connections for ferromagnetic 2-spin systems are much less clear, despite their similarities to anti-ferromagnetic systems. The celebrated Jerrum-Sinclair Markov chain [8] works even if spatial mixing fails. Also, for a fixed degree the uniqueness condition is non-monotone with respect to the external field, which seems to have no meaningful interpretation in terms of computational complexity. However, it is still intriguing whether there are some relationship underneath the apparent disparities among them. We provide some answers to this question. Let β,γbe the (0, 0) and (1, 1) edge interactions respectively (βγ > 1), and λ the external field for spin "0". For graphs with degree bound Δ ≤ Δc + 1 where Δc = √ βγ+1 √ βγ-1 , regardless of the field (even inconsistent fields are allowed), correlation decay always holds and FPTAS exists. If all fields satisfy λ λint c 0, where λint c 0 = (γ/β) b-cc+2 2 , then approximating the partition function is #BIS-hard. Interestingly, unless λc is an integer, neither λc nor λint c is the tight bound in each own respect. We provide examples where correlation decay continues to hold in a small interval beyond λc, and irregular trees in which spatial mixing fails for some λ < λint c