We show that, for a class of planar determinantal point processes (DPP)
X
, the growth of the entanglement entropy
S
(
X
(
Ω
)
)
of
X
on a compact region
Ω
⊂
R
2
d
, is related to the variance
V
X
(
...Ω
)
as follows:
V
X
(
Ω
)
≲
S
X
(
Ω
)
≲
V
X
(
Ω
)
.
Therefore, such DPPs satisfy an
area law
S
X
g
(
Ω
)
≲
∂
Ω
, where
∂
Ω
is the boundary of
Ω
if they are of
Class I hyperuniformity
(
V
X
(
Ω
)
≲
∂
Ω
), while the
area law is violated
if they are of
Class II hyperuniformity
(as
L
→
∞
,
V
X
(
L
Ω
)
∼
C
Ω
L
d
-
1
log
L
). As a result, the entanglement entropy of Weyl–Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
We confirm Flandrin’s prediction for the expected average of local maxima of spectrograms of complex white noise with Gaussian windows (Gaussian spectrograms or, equivalently, modulus of weighted ...Gaussian Entire Functions), a consequence of the conjectured double honeycomb mean model for the network of zeros and local maxima, where the area of local maxima centered hexagons is three times larger than the area of zero centered hexagons. More precisely, we show that Gaussian spectrograms, normalized such that their expected density of zeros is 1, have an expected density of 5/3 critical points, among those 1/3 are local maxima, and 4/3 saddle points, and compute the distributions of ordinate values (heights) for spectrogram local extrema. This is done by first writing the spectrograms in terms of Gaussian Entire Functions (GEFs). The extrema are considered under the translation invariant derivative of the Fock space (which in this case coincides with the Chern connection from complex differential geometry). We also observe that the critical points of a GEF are precisely the zeros of a Gaussian random function in the first higher Landau level. We discuss natural extensions of these Gaussian random functions: Gaussian Weyl–Heisenberg functions and Gaussian bi-entire functions. The paper also reviews recent results on the applications of white noise spectrograms, connections between several developments, and is partially intended as a pedestrian introduction to the topic.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Using Gabor analysis, we give a complete characterization of all lattice sampling and interpolating sequences in the Fock space of polyanalytic functions, displaying a “Nyquist rate” which increases ...with
n, the degree of polyanaliticity of the space. Such conditions are equivalent to sharp lattice density conditions for certain vector-valued Gabor systems, namely superframes and Gabor super-Riesz sequences with Hermite windows, and in the case of superframes they were studied recently by Gröchenig and Lyubarskii. The proofs of our main results use variations of the Janssen–Ron–Shen duality principle and reveal a duality between sampling and interpolation in polyanalytic spaces, and multiple interpolation and sampling in analytic spaces. To connect these topics we introduce the
polyanalytic Bargmann transform, a unitary mapping between vector-valued Hilbert spaces and polyanalytic Fock spaces, which extends the Bargmann transform to polyanalytic spaces. Motivated by this connection, we discuss a vector-valued version of the Gabor transform. These ideas have natural applications in the context of multiplexing of signals. We also point out that a recent result of Balan, Casazza and Landau, concerning density of Gabor frames, has important consequences for the Gröchenig–Lyubarskii conjecture on the density of Gabor frames with Hermite windows.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
We provide a solution to Perelomov's 1972 problem concerning the existence of a phase transition (known in signal analysis as ‘Nyquist rate’) determining the basis properties of certain affine ...coherent states labelled by Fuchsian groups. As suggested by Perelomov, the transition is given according to the hyperbolic volume of the fundamental region. The solution is a more general form (in phase space) of the PSL(2,R) variant of a 1989 conjecture of Kristian Seip about wavelet frames, where the same value of ‘Nyquist rate’ is obtained as the trace of a certain localization operator. The proof consists of first connecting the problem to the theory of von Neumann algebras, by introducing a new class of projective representations of PSL(2,R) acting on non-analytic Bergman-type spaces. We then adapt to this setting a new method for computing von Neumann dimensions, due to Sir Vaughan Jones. Our solution contains necessary conditions in the form of a ‘Nyquist rate’ dividing frames from Riesz sequences of coherent states and sampling from interpolating sequences. They hold for an infinite sequence of spaces of polyanalytic functions containing the eigenspaces of the Maass operator and their orthogonal sums. Within mild boundaries, we show that our result is best possible, by characterizing our sequence of function spaces as the only invariant spaces under the non-analytic PSL(2,R)-representations.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
5.
On accumulated spectrograms Abreu, Luís Daniel; Gröchenig, Karlheinz; Romero, José Luis
Transactions of the American Mathematical Society,
05/2016, Volume:
368, Issue:
5
Journal Article
Peer reviewed
Open access
We study the eigenvalues and eigenfunctions of the time-frequency localization operator H_\Omega of the time-frequency plane. The eigenfunctions are the appropriate prolate spheroidal functions for ...an arbitrary domain \Omega \subseteq \mathbb{R}^{2d} in 1-\delta , 1 up to an error term depending on the perimeter of the boundary of \Omega . We derive asymptotic, non-asymptotic, and weak- L^2 can be approximated solely from the spectrograms of eigenfunctions without information about their phase.
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BFBNIB, INZLJ, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK, ZRSKP
Background
Incisional hernias have an impact on patients’ quality of life and on health care finances. Because of high recurrence rates despite mesh repair, the prevention of incisional hernias with ...prophylactic mesh reinforcement is currently a topic of interest. But only 15% of surgeons are implementing it, mainly because of fear for mesh complications and disbelief in the benefits. The goal of this systematic review is to evaluate the effectiveness and safety of prophylactic mesh in adult patients after midline laparotomy.
Methods
An extensive literature search was performed in PubMed, Embase and CENTRAL until 9/5/2020 for RCTs and cohort studies regarding mesh reinforcement versus primary suture closure of a midline laparotomy. The quality of the articles was analyzed using the Scottish Intercollegiate Guidelines Network checklists. Revman 5 was used to perform a meta-analysis.
Results
Twenty-three articles were found with a total of 1633 patients in the mesh reinforcement group and 1533 in the primary suture group. An odds ratio for incisional hernia incidence of 0.37 (95% CI = 0.30, 0.46,
p
< 0.01) with RCTs and of 0.15 (95% CI = 0.09,0.25,
p
< 0.01) in cohort studies was calculated. Seroma rate shows a significant odds ratio of 2.18 (95% CI = 1.45, 3.29,
p
< 0.01) in favor of primary suture. No increase was found regarding other complications.
Conclusion
The evidence for the use of prophylactic mesh reinforcement is overwhelming with a significant reduction in incisional hernia rate, but implementation in daily clinical practice remains limited. Instead of putting patients at risk for incisional hernia formation and subsequent complications, surgeons should question their arguments why not to use mesh reinforcement, specifically in high-risk patients.
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EMUNI, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
PURPOSEWe evaluated 5-year oncologic and functional outcomes of hemigland cryoablation of localized prostate cancer. MATERIALS AND METHODSWe reviewed the records of 160 consecutive men who underwent ...hemigland cryoablation of localized prostate cancer. Recurrent and/or residual clinically significant prostate cancer was defined as Grade Group 2 or greater on followup biopsy. A prostate specific antigen nadir plus 2 ng/ml according to the Phoenix criteria was used to define biochemical failure. Radical treatment was defined as any whole gland therapy. Treatment failure was defined as any radical and/or whole gland treatment, systemic therapy initiation, metastasis or prostate cancer specific mortality. The study primary end point was treatment failure-free survival. The secondary end points were survival free of biochemical failure, clinically significant prostate cancer and radical treatment. Followup biopsy and functional outcomes were also evaluated. Statistical analysis included the Kaplan-Meier method, and univariate and multivariable Cox and logistic regression with significance considered at p <0.05. RESULTSMedian patient age was 67 years, baseline prostate specific antigen was 6.3 ng/ml and followup was 40 months. A total of 131 patients (82%) had D'Amico intermediate (66%) or high risk (16%) prostate cancer. At 5 years the treatment failure-free survival rate was 85%, the biochemical failure-free survival rate was 62% and the survival rate free of clinically significant prostate cancer was 89%. Higher baseline prostate specific antigen independently predicted treatment failure (p <0.001), biochemical failure (p=0.048), recurrence and radical treatment (p <0.01). Grade Group 3 or greater independently predicted treatment failure (p=0.04). The metastasis-free survival rate was 100% at 5 years. Pad-free continence and potency (erections sufficient for intercourse) were retained in 97% and 73% of patients, respectively. There was no rectal fistula or mortality. CONCLUSIONSHemigland cryoablation of localized prostate cancer provides effective midterm oncologic outcomes with good continence and potency. Patients with higher baseline prostate specific antigen are at increased risk for biochemical failure, recurrent cancer and treatment failure.
Background
Laparoscopic liver surgery is expanding worldwide, but further evidence is needed to assess safety and efficacy of laparoscopic major hepatectomy. The study analyzes perioperative outcomes ...of pure laparoscopic versus open major hepatectomies matched by the propensity score method.
Methods
From 2005 to 2017, 268 major hepatectomies were performed of which 73 were laparoscopic. After a 1:1 propensity score matching, 59 laparoscopic right and left hepatectomies were compared to 59 open. The matching was based on age, gender, year of procedure, BMI, ASA score, underlying liver disease, previous abdominal surgery, type of hepatectomy, preoperative chemotherapy, number, dimension and nature of lesions. An intention-to-treat analysis and a per-protocol analysis were carried out.
Results
Mean surgical time was 315 min in the laparoscopic group and 292.5 min in the open group (
p
= 0.039); conversion rate in laparoscopy was 20.3%; blood loss was 480 ml (50–3000) versus 550 ml (50–2600), respectively, for laparoscopic and open (
p
= 0.577). Lengths of postoperative analgesia and hospital stay were shorter in the laparoscopic group (
p
= 0.0001 and 0.024, respectively). Postoperative complications occurred in 11.9% of laparoscopic cases and in 25.4% of open cases (
p
= 0.098). Median Comprehensive Complication Index was 26.2 (8.7–54.2) in the open group versus 20.9 (8.7–66.2) in open (
p
= 0.368). Per-protocol analysis showed a better trend in favor of laparoscopy concerning surgical time.
Conclusions
Laparoscopic major hepatectomies are safe and feasible procedures allowing a similar complication rate with a shorter hospital stay and diminished postoperative pain with respect to the standard approach.
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EMUNI, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Weyl–Heisenberg ensembles are translation-invariant determinantal point processes on
R
2
d
associated with the Schrödinger representation of the Heisenberg group, and include as examples the Ginibre ...ensemble and the polyanalytic ensembles, which model the higher Landau levels in physics. We introduce finite versions of the Weyl–Heisenberg ensembles and show that they behave analogously to the finite Ginibre ensembles. More specifically, guided by the observation that the Ginibre ensemble with
N
points is asymptotically close to the restriction of the infinite Ginibre ensemble to the disk of area
N
, we define finite WH ensembles as adequate finite approximations of the restriction of infinite WH ensembles to a given domain
Ω
. We provide a precise rate for the convergence of the corresponding one-point intensities to the indicator function of
Ω
, as
Ω
is dilated and the process is rescaled proportionally (thermodynamic regime). The construction and analysis rely neither on explicit formulas nor on the asymptotics for orthogonal polynomials, but rather on phase-space methods. Second, we apply our construction to study the pure finite Ginibre-type polyanalytic ensembles, which model finite particle systems in a single Landau level, and are defined in terms of complex Hermite polynomials. On a technical level, we show that finite WH ensembles provide an approximate model for finite polyanalytic Ginibre ensembles, and we quantify the corresponding deviation. By means of this asymptotic description, we derive estimates for the rate of convergence of the one-point intensity of polyanalytic Ginibre ensembles in the thermodynamic limit.
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DOBA, EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, IZUM, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, SIK, UILJ, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Multiparametric magnetic resonance imaging (mpMRI) has become increasingly important for the clinical assessment of prostate cancer (PCa), but its interpretation is generally variable due to its ...relatively subjective nature. Radiomics and classification methods have shown potential for improving the accuracy and objectivity of mpMRI-based PCa assessment. However, these studies are limited to a small number of classification methods, evaluation using the AUC score only, and a non-rigorous assessment of all possible combinations of radiomics and classification methods. This paper presents a systematic and rigorous framework comprised of classification, cross-validation and statistical analyses that was developed to identify the best performing classifier for PCa risk stratification based on mpMRI-derived radiomic features derived from a sizeable cohort. This classifier performed well in an independent validation set, including performing better than PI-RADS v2 in some aspects, indicating the value of objectively interpreting mpMRI images using radiomics and classification methods for PCa risk assessment.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
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