In this paper we apply ideas from the theory of Uniform Distribution of sequences to Functional Analysis and then drawing inspiration from the consequent results, we study concepts and results in ...Uniform Distribution itself. so let
E
be a Banach space. then we prove:
If
F
is a bounded subset of
E
and
x
∈
co
¯
(
F
)
(= the closed convex hull of
F
), then there is a sequence (
x
n
) ⊆
F
which is Cesàro summable to
x
.
If
E
is separable,
F
⊆
E
* bounded and
f
∈
co
¯
w
∗
(
F
)
, then there is a sequence (
f
n
) ⊆
F
whose sequence of arithmetic means
f
1
+
⋯
f
N
N
,
N
≥ 1 weak*-converges to
f
.
By the aid of the Krein-Milman theorem, both (a) and (b) have interesting implications for closed, convex and bounded subsets Ω of
E
such that
Ω
=
co
¯
(
ex
Ω
)
and for weak* compact and convex subsets of
E
*. Of particular interest is the case when Ω =
B
C
(
K
)*
, where
K
is a compact metric space.
By further expanding the previous ideas and results, we are able to generalize a classical theorem of Uniform Distribution which is valid for increasing functions φ:
I
=0,1 → ℝ with φ(0) = 0 and φ(1) = 1, for functions φ of bounded variation on
I
with φ(0) = 0 and total variation
V
0
1
φ = 1.
Let
X
be a finite-dimensional Banach space; we introduce and investigate a natural generalization of the concepts of Hadwiger number
H
(
X
) and strict Hadwiger number
H
′
(
X
)
. More precisely, we ...define the antipodal Hadwiger number
H
α
(
X
)
as the largest cardinality of a subset
S
⊆
S
X
, such that
∀
x
≠
y
∈
S
∃
f
∈
B
X
∗
with
1
≤
f
(
x
)
-
f
(
y
)
and
f
(
y
)
≤
f
(
z
)
≤
f
(
x
)
for
z
∈
S
.
The strict antipodal Hadwiger number
H
α
′
(
X
)
is defined analogously. We prove that
H
α
′
(
X
)
=
4
for every Minkowski plane and estimate (or in some cases compute) the numbers
H
α
(
X
)
and
H
α
′
(
X
)
, where
X
=
ℓ
p
n
,
1
<
p
≤
+
∞
and
n
≥
2
. We also show that the number
H
α
′
(
X
)
grows exponentially in
dim
X
.
We show that every Banach space X has an infinite equilateral set and also that if X, then it can be renormed so as to admit an equilateral set of equal size.
Scientifically defined in 1880 by the Curie brothers, piezoelectricity - from the Greek piezein, meaning to press (squeeze), and ilektron, meaning amber, a material with electrostatic properties - is ...a phenomenon with many applications. The related piezoelectric materials have been undergoing a long-lasting evolution over the years until today. The field of organic and inorganic piezoelectric materials is continuously expanding in terms of new substances used, new structures, and new applications. The seven chapters of this book present modern aspects and technological advances in the field of piezoelectric materials and applications. To present a balanced view of the field, some chapters focus on new piezoelectric materials and structures, while others examine interesting applications of piezoelectric sensors, energy harvesters, and actuators.
Background and Aim: Adefovir dipivoxil (ADV) is effective in lamivudine (LAM)‐resistant hepatitis B e antigen‐negative (HBeAg‐) chronic hepatitis B (CHB). However, it is unclear whether LAM ...treatment should be continued in these patients. We aimed to compare the long‐term efficacy of adding ADV to ongoing LAM treatment versus switching to ADV monotherapy in LAM‐resistant HBeAg‐ CHB.
Methods: Sixty LAM‐resistant patients with HBeAg‐ CHB were randomly assigned (3:1) to combination therapy (10 mg ADV once daily plus ongoing LAM at 100 mg once daily n = 45) or 10 mg ADV monotherapy once daily (n = 15). Virological and biochemical responses were defined as hepatitis B virus (HBV)–DNA <400 copies/mL and as normalization of alanine aminotransferase levels, respectively.
Results: The median follow‐up time was 53 months (range 20–60 months). A virological response was observed in 38/45 (84.4%) and 11/15 (73.3%) patients in the ADV/LAM and ADV monotherapy groups, respectively (P = 0.56). Biochemical response rates were higher in the ADV/LAM group than in the ADV monotherapy group (90.9% vs 57.1%, respectively; P = 0.01). In the ADV/LAM group, serum HBV–DNA remained undetectable in all patients who achieved a virological response (n = 38). In the ADV monotherapy group, virological breakthrough occurred in four of the 11 patients who achieved a virological response (36.4%; P < 0.001 vs the ADV/LAM group, log–rank test). In addition, two patients in each group who did not achieve a virological response eventually developed ADV resistance.
Conclusions: Adding ADV to LAM is more effective than switching to ADV monotherapy in LAM‐resistant patients with HBeAg‐ CHB.
On Data Publishing with Clustering Preservation Vlachos, Michail; Schneider, Johannes; Vassiliadis, Vassilios G.
ACM transactions on knowledge discovery from data,
04/2015, Letnik:
9, Številka:
3
Journal Article
Recenzirano
The emergence of cloud-based storage services is opening up new avenues in data exchange and data dissemination. This has amplified the interest in right-protection mechanisms to establish ownership ...in the event of data leakage. Current right-protection technologies, however, rarely provide strong guarantees on dataset utility after the protection process. This work presents techniques that explicitly address this topic and provably preserve the outcome of certain mining operations. In particular, we take special care to guarantee that the outcome of hierarchical clustering operations remains the same before and after right protection. Our approach considers all prevalent hierarchical clustering variants: single-, complete-, and average-linkage. We imprint the ownership in a dataset using watermarking principles, and we derive tight bounds on the expansion/contraction of distances incurred by the process. We leverage our analysis to design fast algorithms for right protection without exhaustively searching the vast design space. Finally, because the right-protection process introduces a user-tunable distortion on the dataset, we explore the possibility of using this mechanism for data obfuscation. We quantify the tradeoff between obfuscation and utility for spatiotemporal datasets and discover very favorable characteristics of the process. An additional advantage is that when one is interested in both right-protecting and obfuscating the original data values, the proposed mechanism can accomplish both tasks simultaneously.
Over recent decades, a constantly growing interest in the field of portable electronic devices has been observed. Recent developments in the scientific areas of integrated circuits and sensing ...technologies have enabled realization and design of lightweight low-power wearable sensing systems that can be of great use, especially for continuous health monitoring and performance recording applications. However, to facilitate wide penetration of such systems into the market, the issue of ensuring their seamless and reliable power supply still remains a major concern. In this work, the performance of a thermoelectric generator, able to exploit the temperature difference established between the human body and the environment, has been examined computationally using ANSYS 14.0 finite-element modeling (FEM) software, as a means for providing the necessary power to various portable electronic systems. The performance variation imposed due to different thermoelement geometries has been estimated to identify the most appropriate solution for the considered application. Furthermore, different ambient temperature and heat exchange conditions between the cold side of the generator and the environment have been investigated. The computational analysis indicated that power output in the order of 1.8 mW can be obtained by a 100-cm
2
system, if specific design criteria can be fulfilled.
•A wearable magnetic sensing device has been developed and tested.•Magnetostrictive materials of ribbon and wire type have been employed.•Temperature as well as MDL material non-uniformity issues ...have been examined.
Nowadays, the ever growing use of electronic equipment in everyday life raises issues regarding the safety of specific population groups, such as patients carrying EMI sensitive implantable devices (e.g. cardiac pacemakers, surgical stents, etc.). In this respect, the need for wearable magnetic monitoring systems, able of detecting the presence of possibly hazardous magnetic fields of various different origins may become obvious. In this work, a wearable magnetic sensing device has been constructed in order to assess its ability to identify the presence of static magnetic fields of magnetic flux density up to 6 Gauss. Magnetostrictive delay lines (MDLs) have been employed as the sensing elements, due to their fibrous form and minimal thickness, which allows integration in textile and clothing products. Two different amorphous magnetostrictive materials, in ribbon and wire form respectively, have been tested in order to reveal the most appropriate solution for the application under consideration. Moreover, different performance aspects, such as uniformity of sensor’s response as well as temperature effects have been examined. The experimental results indicate that the proposed system can effectively operate within the required magnetic flux density range. Moreover, the fibrous character of the MDL makes it a perfectly suitable material for wearable applications.
The phenomenon of quasi-complete separation that appears in the identification of the neuromuscular system called muscle spindle by a logistic regression model is considered. The system responds when ...it is affected by a number of stimuli. Both the response and the stimuli are very long binary sequences of events. In the logistic model, three functions are of special interest: the threshold, the recovery and the summation functions. The maximum likelihood estimates are obtained efficiently and very fast by using the penalized likelihood function. A validity test for the fitted model based on the randomized quantile residuals is proposed. The validity test is transformed to a goodness of fit test and the use of Q–Q plot is also discussed.
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